Solutions of Several Coupled Discrete Models in terms of Lame Polynomials of Order One and Two

Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lame polynomials of order one and two. Some of the models discussed are (i) coupled Salerno model, (ii) coupled Ablowitz-Ladik model, (iii) coupled saturated discrete nonlinear Schrodinger equation, (iv) coupled phi4 model, and (v) coupled phi6 model. Furthermore, we show that most of these coupled models in fact also possess an even broader class of exact solutions.Comment: 31 pages, to appear in Pramana (Journal of Physics) 201

Electric control of magnetism at room temperature

In the single-phase multiferroics, the coupling between electric polarization (P) and magnetization (M) would enable the magnetoelectric (ME) effect, namely M induced and modulated by E, and conversely P by H. Especially, the manipulation of magnetization by an electric field at room-temperature is of great importance in technological applications, such as new information storage technology, four-state logic device, magnetoelectric sensors, low-power magnetoelectric device and so on. Furthermore, it can reduce power consumption and realize device miniaturization, which is very useful for the practical applications. In an M-type hexaferrite SrCo2Ti2Fe8O19, large magnetization and electric polarization were observed simultaneously at room-temperature. Moreover, large effect of electric field-controlled magnetization was observed even without magnetic bias field. These results illuminate a promising potential to apply in magnetoelectric devices at room temperature and imply plentiful physics behind them

Nonlinear deterministic equations in biological evolution

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy

Positional Signaling and Expression of ENHANCER OF TRY AND CPC1 Are Tuned to Increase Root Hair Density in Response Phosphate Deficiency in Arabidopsis thaliana

Phosphate (Pi) deficiency induces a multitude of responses aimed at improving the acquisition of Pi, including an increased density of root hairs. To understand the mechanisms involved in Pi deficiency-induced alterations of the root hair phenotype in Arabidopsis (Arabidopsis thaliana), we analyzed the patterning and length of root epidermal cells under control and Pi-deficient conditions in wild-type plants and in four mutants defective in the expression of master regulators of cell fate, CAPRICE (CPC), ENHANCER OF TRY AND CPC 1 (ETC1), WEREWOLF (WER) and SCRAMBLED (SCM). From this analysis we deduced that the longitudinal cell length of root epidermal cells is dependent on the correct perception of a positional signal (‘cortical bias’) in both control and Pi-deficient plants; mutants defective in the receptor of the signal, SCM, produced short cells characteristic of root hair-forming cells (trichoblasts). Simulating the effect of cortical bias on the time-evolving probability of cell fate supports a scenario in which a compromised positional signal delays the time point at which non-hair cells opt out the default trichoblast pathway, resulting in short, trichoblast-like non-hair cells. Collectively, our data show that Pi-deficient plants increase root hair density by the formation of shorter cells, resulting in a higher frequency of hairs per unit root length, and additional trichoblast cell fate assignment via increased expression of ETC1

Application of layered poly (L-lactic acid) cell free scaffold in a rabbit rotator cuff defect model

<p>Abstract</p> <p>Background</p> <p>This study evaluated the application of a layered cell free poly (L-lactic acid) (PLLA) scaffold to regenerate an infraspinatus tendon defect in a rabbit model. We hypothesized that PLLA scaffold without cultivated cells would lead to regeneration of tissue with mechanical properties similar to reattached infraspinatus without tendon defects.</p> <p>Methods</p> <p>Layered PLLA fabric with a smooth surface on one side and a pile-finished surface on the other side was used. Novel form of layered PLLA scaffold was created by superimposing 2 PLLA fabrics. Defects of the infraspinatus tendon were created in 32 rabbits and the PLLA scaffolds were transplanted, four rabbits were used as normal control. Contralateral infraspinatus tendons were reattached to humeral head without scaffold implantation. Histological and mechanical evaluations were performed at 4, 8, and 16 weeks after operation.</p> <p>Results</p> <p>At 4 weeks postoperatively, cell migration was observed in the interstice of the PLLA fibers. Regenerated tissue was directly connected to the bone composed mainly of type III collagen, at 16 weeks postoperatively. The ultimate failure load increased in a time-dependent manner and no statistical difference was seen between normal infraspinatus tendon and scaffold group at 8 and 16 weeks postoperatively. There were no differences between scaffold group and reattach group at each time of point. The stiffness did not improve significantly in both groups.</p> <p>Conclusions</p> <p>A novel form of layered PLLA scaffold has the potential to induce cell migration into the scaffold and to bridge the tendon defect with mechanical properties similar to reattached infraspinatus tendon model.</p

Inferring stabilizing mutations from protein phylogenies : application to influenza hemagglutinin

One selection pressure shaping sequence evolution is the requirement that a protein fold with sufficient stability to perform its biological functions. We present a conceptual framework that explains how this requirement causes the probability that a particular amino acid mutation is fixed during evolution to depend on its effect on protein stability. We mathematically formalize this framework to develop a Bayesian approach for inferring the stability effects of individual mutations from homologous protein sequences of known phylogeny. This approach is able to predict published experimentally measured mutational stability effects (ΔΔG values) with an accuracy that exceeds both a state-of-the-art physicochemical modeling program and the sequence-based consensus approach. As a further test, we use our phylogenetic inference approach to predict stabilizing mutations to influenza hemagglutinin. We introduce these mutations into a temperature-sensitive influenza virus with a defect in its hemagglutinin gene and experimentally demonstrate that some of the mutations allow the virus to grow at higher temperatures. Our work therefore describes a powerful new approach for predicting stabilizing mutations that can be successfully applied even to large, complex proteins such as hemagglutinin. This approach also makes a mathematical link between phylogenetics and experimentally measurable protein properties, potentially paving the way for more accurate analyses of molecular evolution

Why Is the Correlation between Gene Importance and Gene Evolutionary Rate So Weak?

One of the few commonly believed principles of molecular evolution is that functionally more important genes (or DNA sequences) evolve more slowly than less important ones. This principle is widely used by molecular biologists in daily practice. However, recent genomic analysis of a diverse array of organisms found only weak, negative correlations between the evolutionary rate of a gene and its functional importance, typically measured under a single benign lab condition. A frequently suggested cause of the above finding is that gene importance determined in the lab differs from that in an organism's natural environment. Here, we test this hypothesis in yeast using gene importance values experimentally determined in 418 lab conditions or computationally predicted for 10,000 nutritional conditions. In no single condition or combination of conditions did we find a much stronger negative correlation, which is explainable by our subsequent finding that always-essential (enzyme) genes do not evolve significantly more slowly than sometimes-essential or always-nonessential ones. Furthermore, we verified that functional density, approximated by the fraction of amino acid sites within protein domains, is uncorrelated with gene importance. Thus, neither the lab-nature mismatch nor a potentially biased among-gene distribution of functional density explains the observed weakness of the correlation between gene importance and evolutionary rate. We conclude that the weakness is factual, rather than artifactual. In addition to being weakened by population genetic reasons, the correlation is likely to have been further weakened by the presence of multiple nontrivial rate determinants that are independent from gene importance. These findings notwithstanding, we show that the principle of slower evolution of more important genes does have some predictive power when genes with vastly different evolutionary rates are compared, explaining why the principle can be practically useful despite the weakness of the correlation

Accuracy of breeding values of 'unrelated' individuals predicted by dense SNP genotyping

<p>Abstract</p> <p>Background</p> <p>Recent developments in SNP discovery and high throughput genotyping technology have made the use of high-density SNP markers to predict breeding values feasible. This involves estimation of the SNP effects in a training data set, and use of these estimates to evaluate the breeding values of other 'evaluation' individuals. Simulation studies have shown that these predictions of breeding values can be accurate, when training and evaluation individuals are (closely) related. However, many general applications of genomic selection require the prediction of breeding values of 'unrelated' individuals, i.e. individuals from the same population, but not particularly closely related to the training individuals.</p> <p>Methods</p> <p>Accuracy of selection was investigated by computer simulation of small populations. Using scaling arguments, the results were extended to different populations, training data sets and genome sizes, and different trait heritabilities.</p> <p>Results</p> <p>Prediction of breeding values of unrelated individuals required a substantially higher marker density and number of training records than when prediction individuals were offspring of training individuals. However, when the number of records was 2*N_e*L and the number of markers was 10*N_e*L, the breeding values of unrelated individuals could be predicted with accuracies of 0.88 – 0.93, where N_eis the effective population size and L the genome size in Morgan. Reducing this requirement to 1*N_e*L individuals, reduced prediction accuracies to 0.73–0.83.</p> <p>Conclusion</p> <p>For livestock populations, 1N_eL requires about ~30,000 training records, but this may be reduced if training and evaluation animals are related. A prediction equation is presented, that predicts accuracy when training and evaluation individuals are related. For humans, 1N_eL requires ~350,000 individuals, which means that human disease risk prediction is possible only for diseases that are determined by a limited number of genes. Otherwise, genotyping and phenotypic recording need to become very common in the future.</p