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

Algebraic entropy for semi-discrete equations

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of integrability for this type of equations

HCMV pUL135 remodels the actin cytoskeleton to impair immune recognition of infected cells

Immune evasion genes help human cytomegalovirus (HCMV) establish lifelong persistence. Without immune pressure, laboratory-adapted HCMV strains have undergone genetic alterations. Among these, the deletion of the UL/b’ domain is associated with loss of virulence. In a screen of UL/b’, we identified pUL135 as a protein responsible for the characteristic cytopathic effect of clinical HCMV strains that also protected from natural killer (NK) and T cell attack. pUL135 interacted directly with abl interactor 1 (ABI1) and ABI2 to recruit the WAVE2 regulatory complex to the plasma membrane, remodel the actin cytoskeleton and dramatically reduce the efficiency of immune synapse (IS) formation. An intimate association between F-actin filaments in target cells and the IS was dispelled by pUL135 expression. Thus, F-actin in target cells plays a critical role in synaptogenesis, and this can be exploited by pathogens to protect against cytotoxic immune effector cells. An independent interaction between pUL135 and talin disrupted cell contacts with the extracellular matrix

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

Interleukin-6, tumour necrosis factor α and interleukin-1β in patients with renal cell carcinoma

As regulators of malignant cell behaviour and communication with stroma, cytokines have proved useful in understanding cancer biology and developing novel therapies. In renal cell carcinoma, patients with inflammatory reactions are known to have poor prognosis. In order to elucidate the relation between renal cell carcinoma and the host, serum levels of inflammatory cytokines, interleukin-6, tumour necrosis factor α, interleukin-1β, were measured. One hundred and twenty-two patients with renal cell carcinoma and 21 healthy control subjects were studied, and serum cytokine levels were measured using a highly sensitive ELISA kit. As a result, in the control group, interleukin-6, tumour necrosis factor α and interleukin-1β levels were 1.79±2.03, 2.74±0.94 and 0.16±0.17 pg ml−1, respectively. In the renal cell carcinoma patients, they were 8.91±13.12, 8.44±4.15 and 0.53±0.57 pg ml−1, respectively, and significantly higher. In the comparison of stage, interleukin-6 level was significantly higher in the stage IV group compared to the other stage groups including the control group, while tumour necrosis factor α level was significantly higher in each stage group compared to the control group. As for grade, interleukin-6 level was significantly higher in the grade 3 group compared to the control, grade 1 and grade 2 groups, while tumour necrosis factor α level was significantly higher in each grade group compared to the control group. All cytokines had a positive correlation with tumour size. In regard to the correlation with CRP, all cytokines had a positive correlation with CRP, while interleukin-6 had a particularly strong correlation. In conclusion, interleukin-6 may be one of the factors for the poor prognosis of patients with renal cell carcinoma. In addition, tumour necrosis factor α may be useful in the early diagnosis of renal cell carcinoma and post-operative follow-up

Propagating Cell-Membrane Waves Driven by Curved Activators of Actin Polymerization

Cells exhibit propagating membrane waves which involve the actin cytoskeleton. One type of such membranal waves are Circular Dorsal Ruffles (CDR) which are related to endocytosis and receptor internalization. Experimentally, CDRs have been associated with membrane bound activators of actin polymerization of concave shape. We present experimental evidence for the localization of convex membrane proteins in these structures, and their insensitivity to inhibition of myosin II contractility in immortalized mouse embryo fibroblasts cell cultures. These observations lead us to propose a theoretical model which explains the formation of these waves due to the interplay between complexes that contain activators of actin polymerization and membrane-bound curved proteins of both types of curvature (concave and convex). Our model predicts that the activity of both types of curved proteins is essential for sustaining propagating waves, which are abolished when one type of curved activator is removed. Within this model waves are initiated when the level of actin polymerization induced by the curved activators is higher than some threshold value, which allows the cell to control CDR formation. We demonstrate that the model can explain many features of CDRs, and give several testable predictions. This work demonstrates the importance of curved membrane proteins in organizing the actin cytoskeleton and cell shape

Do mammals make all their own inositol hexakisphosphate?

A highly specific and sensitive mass assay for inositol hexakisphosphate (InsP6) was characterized. This centres around phosphorylating InsP6 with [32P]ATP using a recombinant InsP6 kinase from Giardia lambia, followed by HPLC of the 32P-labelled products with an internal [3H]InsP7 standard. This assay was used to quantify InsP6 levels in a variety of biological samples. Concentrations of InsP6 in rat tissues varied from 10–20 μM (assuming 64% of wet weight of tissue is cytosol water), whereas using the same assumption axenic Dictyostelium discoideum cells contained 352±11 μM InsP6. HeLa cells were seeded at low density and grown to confluence, at which point they contained InsP6 levels per mg of protein similar to rat tissues. This amounted to 1.952±0.117 nmol InsP6 per culture dish, despite the cells being grown in serum shown to contain no detectable (less than 20 pmol per dish) InsP6. These results demonstrate that mammalian cells synthesize all their own InsP6. Human blood was analysed, and although the white cell fraction contained InsP6 at a concentration comparable with other tissues, in serum and platelet-free plasma no InsP6 was detected (<1 nM InsP6). Human urine was also examined, and also contained no detectable (<5 nM) InsP6. These results suggest that dietary studies purporting to measure InsP6 at micromolar concentrations in human plasma or urine may not have been quantifying this inositol phosphate. Therefore claims that administrating InsP6 in the diet or applying it topically can produce health benefits by increasing extracellular InsP6 levels may require reassessment