Scaling of Star Polymers with one to 80 Arms

We present large statistics simulations of 3-dimensional star polymers with up to $f=80$ arms, and with up to 4000 monomers per arm for small values of $f$. They were done for the Domb-Joyce model on the simple cubic lattice. This is a model with soft core exclusion which allows multiple occupancy of sites but punishes each same-site pair of monomers with a Boltzmann factor $v<1$. We use this to allow all arms to be attached at the central site, and we use the `magic' value $v=0.6$ to minimize corrections to scaling. The simulations are made with a very efficient chain growth algorithm with resampling, PERM, modified to allow simultaneous growth of all arms. This allows us to measure not only the swelling (as observed from the center-to-end distances), but also the partition sum. The latter gives very precise estimates of the critical exponents $\gamma_f$. For completeness we made also extensive simulations of linear (unbranched) polymers which give the best estimates for the exponent $\gamma$.Comment: 7 pages, 7 figure

A review of Monte Carlo simulations of polymers with PERM

In this review, we describe applications of the pruned-enriched Rosenbluth method (PERM), a sequential Monte Carlo algorithm with resampling, to various problems in polymer physics. PERM produces samples according to any given prescribed weight distribution, by growing configurations step by step with controlled bias, and correcting "bad" configurations by "population control". The latter is implemented, in contrast to other population based algorithms like e.g. genetic algorithms, by depth-first recursion which avoids storing all members of the population at the same time in computer memory. The problems we discuss all concern single polymers (with one exception), but under various conditions: Homopolymers in good solvents and at the $\Theta$ point, semi-stiff polymers, polymers in confining geometries, stretched polymers undergoing a forced globule-linear transition, star polymers, bottle brushes, lattice animals as a model for randomly branched polymers, DNA melting, and finally -- as the only system at low temperatures, lattice heteropolymers as simple models for protein folding. PERM is for some of these problems the method of choice, but it can also fail. We discuss how to recognize when a result is reliable, and we discuss also some types of bias that can be crucial in guiding the growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011

Lysophosphatidic acid and sphingosine-1-phosphate promote morphogenesis and block invasion of prostate cancer cells in three-dimensional organotypic models

Normal prostate and some malignant prostate cancer (PrCa) cell lines undergo acinar differentiation and form spheroids in three-dimensional (3-D) organotypic culture. Acini formed by PC-3 and PC-3M, less pronounced also in other PrCa cell lines, spontaneously undergo an invasive switch, leading to the disintegration of epithelial structures and the basal lamina, and formation of invadopodia. This demonstrates the highly dynamic nature of epithelial plasticity, balancing epithelial-to-mesenchymal transition against metastable acinar differentiation. This study assessed the role of lipid metabolites on epithelial maturation. PC-3 cells completely failed to form acinar structures in delipidated serum. Adding back lysophosphatidic acid (LPA) and sphingosine-1-phosphate (S1P) rescued acinar morphogenesis and repressed invasion effectively. Blocking LPA receptor 1 (LPAR1) functions by siRNA (small interference RNA) or the specific LPAR1 inhibitor Ki16425 promoted invasion, while silencing of other G-protein-coupled receptors responsive to LPA or S1P mainly caused growth arrest or had no effects. The G-proteins Gα12/13 and Gαi were identified as key mediators of LPA signalling via stimulation of RhoA and Rho kinases ROCK1 and 2, activating Rac1, while inhibition of adenylate cyclase and accumulation of cAMP may be secondary. Interfering with these pathways specifically impeded epithelial polarization in transformed cells. In contrast, blocking the same pathways in non-transformed, normal cells promoted differentiation. We conclude that LPA and LPAR1 effectively promote epithelial maturation and block invasion of PrCa cells in 3-D culture. The analysis of clinical transcriptome data confirmed reduced expression of LPAR1 in a subset of PrCa's. Our study demonstrates a metastasis-suppressor function for LPAR1 and Gα12/13 signalling, regulating cell motility and invasion versus epithelial maturation

Field template-based design and biological evaluation of new sphingosine kinase 1 inhibitors

Purpose: Sphingosine kinase 1 (SK1) is a protooncogenic enzyme expressed in many human tumours and is associated with chemoresistance and poor prognosis. It is a potent therapy target and its inhibition chemosensitises solid tumours. Despite recent advances in SK1 inhibitors synthesis and validation, their clinical safety and chemosensitising options are not well described. In this study, we have designed, synthesised and tested a new specific SK1 inhibitor with a low toxicity profile. Methods: Field template molecular modelling was used for compound design. Lead compounds were tested in cell and mouse cancer models. Results: Field template analysis of three known SK1 inhibitors, SKI-178, 12aa and SK1-I, was performed and compound screening identified six potential new SK1 inhibitors. SK1 activity assays in both cell-free and in vitro settings showed that two compounds were effective SK1 inhibitors. Compound SK-F has potently decreased cancer cell viability in vitro and sensitised mouse breast tumours to docetaxel (DTX) in vivo, without significant whole-body toxicity. Conclusion: Through field template screening, we have identified a new SK1 inhibitor, SK-F, which demonstrated antitumour activity in vitro and in vivo without overt toxicity when combined with DTX