Algebraic entropy and the space of initial values for discrete dynamical systems

A method to calculate the algebraic entropy of a mapping which can be lifted to an isomorphism of a suitable rational surfaces (the space of initial values) are presented. It is shown that the degree of the $n$th iterate of such a mapping is given by its action on the Picard group of the space of initial values. It is also shown that the degree of the $n$th iterate of every Painlev\'e equation in sakai's list is at most $O(n^2)$ and therefore its algebraic entropy is zero.Comment: 10 pages, pLatex fil

On the complexity of some birational transformations

Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions

Phosphoinositide-binding interface proteins involved in shaping cell membranes

The mechanism by which cell and cell membrane shapes are created has long been a subject of great interest. Among the phosphoinositide-binding proteins, a group of proteins that can change the shape of membranes, in addition to the phosphoinositide-binding ability, has been found. These proteins, which contain membrane-deforming domains such as the BAR, EFC/F-BAR, and the IMD/I-BAR domains, led to inward-invaginated tubes or outward protrusions of the membrane, resulting in a variety of membrane shapes. Furthermore, these proteins not only bind to phosphoinositide, but also to the N-WASP/WAVE complex and the actin polymerization machinery, which generates a driving force to shape the membranes

Arp2/3 activity is necessary for efficient formation of E-cadherin adhesive contacts

Classical cadherin adhesion molecules are fundamental determinants of cell-cell recognition that function in cooperation with the actin cytoskeleton. Productive cadherin-based cell recognition is characterized by a distinct morphological process of contact zone extension, where limited initial points of adhesion are progressively expanded into broad zones of contact. We recently demonstrated that E-cadherin ligation recruits the Arp2/3 actin nucleator complex to the plasma membrane in regions where cell contacts are undergoing protrusion and extension. This suggested that Arp2/3 might generate the protrusive forces necessary for cell surfaces to extend upon one another during contact assembly. We tested this hypothesis in mammalian cells by exogenously expressing the CA region of N-WASP. This fragment, which potently inhibits Arp2/3-mediated actin assembly in vitro, also effectively reduced actin assembly at cadherin adhesive contacts. Blocking Arp2/3 activity by this strategy profoundly reduced the ability of cells to extend cadherin adhesive contacts but did not affect cell adhesiveness. These findings demonstrate that Arp2/3 activity is necessary for cells to efficiently extend and assemble cadherin-based adhesive contacts

Peptide Array X-Linking (PAX): A New Peptide-Protein Identification Approach

Many protein interaction domains bind short peptides based on canonical sequence consensus motifs. Here we report the development of a peptide array-based proteomics tool to identify proteins directly interacting with ligand peptides from cell lysates. Array-formatted bait peptides containing an amino acid-derived cross-linker are photo-induced to crosslink with interacting proteins from lysates of interest. Indirect associations are removed by high stringency washes under denaturing conditions. Covalently trapped proteins are subsequently identified by LC-MS/MS and screened by cluster analysis and domain scanning. We apply this methodology to peptides with different proline-containing consensus sequences and show successful identifications from brain lysates of known and novel proteins containing polyproline motif-binding domains such as EH, EVH1, SH3, WW domains. These results suggest the capacity of arrayed peptide ligands to capture and subsequently identify proteins by mass spectrometry is relatively broad and robust. Additionally, the approach is rapid and applicable to cell or tissue fractions from any source, making the approach a flexible tool for initial protein-protein interaction discovery.National Institutes of Health (U.S.) (Grant R21-CA-140030-01

Increased serum hepcidin-25 level and increased tumor expression of hepcidin mRNA are associated with metastasis of renal cell carcinoma

<p>Abstract</p> <p>Background</p> <p>Hepcidin has an important role in iron metabolism. We investigated whether hepcidin was involved in renal cell carcinoma (RCC).</p> <p>Methods</p> <p>We measured serum hepcidin-25 levels in 32 patients by liquid chromatograpy (LC)-mass spectrometry (MS)/MS, and assessed hepcidin mRNA expression in paired tumor and non-tumor tissue samples from the surgical specimens of 53 consecutive patients with RCC by real-time reverse transcription polymerase chain reaction.</p> <p>Results</p> <p>The serum hepcidin-25 level was higher in patients with metastatic RCC than nonmetastatic RCC (<it>P </it>< 0.0001), and was positively correlated with the serum interleukin-6 and C-reactive protein levels (<it>P </it>< 0.001). Expression of hepcidin mRNA was lower in tumor tissues than in non-tumor tissues (<it>P </it>< 0.0001). The serum hepcidin-25 level was not correlated with the expression of hepcidin mRNA in the corresponding tumor tissue specimens from 32 patients. Hepcidin mRNA expression in tumor tissue was correlated with metastatic potential, but not with histological differentiation or tumor stage. Kaplan-Meier analysis showed that over expression of hepcidin mRNA was related to shorter overall survival in RCC patients. Univariate analysis (Cox proportional hazards model) showed that the hepcidin mRNA level was an independent prognostic factor for overall survival.</p> <p>Conclusion</p> <p>Our findings suggest that a high serum hepcidin-25 level may indicate the progression of RCC, and that upregulation of hepcidin mRNA expression in tumor tissue may be related to increased metastatic potential.</p

Scapinin, the Protein Phosphatase 1 Binding Protein, Enhances Cell Spreading and Motility by Interacting with the Actin Cytoskeleton

Copyright (c) 2009 Sagara et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Scapinin, also named phactr3, is an actin and protein phosphatase 1 (PP1) binding protein, which is expressed in the adult brain and some tumor cells. At present, the role(s) of scapinin in the brain and tumors are poorly understood. We show that the RPEL-repeat domain of scapinin, which is responsible for its direct interaction with actin, inhibits actin polymerization in vitro. Next, we established a Hela cell line, where scapinin expression was induced by tetracycline. In these cells, expression of scapinin stimulated cell spreading and motility. Scapinin was colocalized with actin at the edge of spreading cells. To explore the roles of the RPEL-repeat and PP1-binding domains, we expressed wild-type and mutant scapinins as fusion proteins with green fluorescence protein (GFP) in Cos7 cells. Expression of GFP-scapinin (wild type) also stimulated cell spreading, but mutation in the RPEL-repeat domain abolished both the actin binding and the cell spreading activity. PP1-binding deficient mutants strongly induced cell retraction. Long and branched cytoplasmic processes were developed during the cell retraction. These results suggest that scapinin enhances cell spreading and motility through direct interaction with actin and that PP1 plays a regulatory role in scapinin-induced morphological changes.ArticlePLOS ONE. 4(1):e4247 (2009)journal articl

Free Brick1 Is a Trimeric Precursor in the Assembly of a Functional Wave Complex

Background: The Wave complex activates the Arp2/3 complex, inducing actin polymerization in lamellipodia and membrane ruffles. The Wave complex is composed of five subunits, the smallest of which, Brick1/Hspc300 (Brk1), is the least characterized. We previously reported that, unlike the other subunits, Brk1 also exists as a free form. Principal Findings: Here we report that this free form of Brk1 is composed of homotrimers. Using a novel assay in which purified free Brk1 is electroporated into HeLa cells, we were able to follow its biochemical fate in cells and to show that free Brk1 becomes incorporated into the Wave complex. Importantly, incorporation of free Brk1 into the Wave complex was blocked upon inhibition of protein synthesis and incorporated Brk1 was found to associate preferentially with neosynthesized subunits. Brk1 depleted HeLa cells were found to bleb, as were Nap1, Wave2 or ARPC2 depleted cells, suggesting that this blebbing phenotype of Brk1 depleted cells is due to an impairment of the Wave complex function rather than a specific function of free Brk1. Blebs of Brk1 depleted cells were emitted at sites where lamellipodia and membrane ruffles were normally emitted. In Brk1 depleted cells, the electroporation of free Brk1 was sufficient to restore Wave complex assembly and to rescue the blebbing phenotype. Conclusion: Together these results establish that the free form of Brk1 is an essential precursor in the assembly of