Conservation laws of scaling-invariant field equations

A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities having non-zero scaling weight. Applications to several soliton equations, fluid flow and nonlinear wave equations, Yang-Mills equations and the Einstein gravitational field equations are considered.Comment: 18 pages, published version in J. Phys. A:Math. and Gen. (2003). Added discussion of vorticity conservation laws for fluid flow; corrected recursion formula and operator for vector mKdV conservation law

Matrix metalloproteinases and their tissue inhibitors after selective laser trabeculoplasty in pseudoexfoliative secondary glaucoma

<p>Abstract</p> <p>Background</p> <p>The aim of this study was to assess changes in metalloproteinases (MMP-2) and tissue inhibitor of metalloproteinases (TIMP-2) following selective laser trabeculoplasty (SLT) in patients with pseudoexfoliative glaucoma (PEXG).</p> <p>Methods</p> <p>We enrolled 15 patients with PEXG and cataracts (PEXG-C group) and good intraocular pressure (IOP) controlled with β-blockers and dorzolamide eye drops who were treated by cataract phacoemulsification and 15 patients with pseudoexfoliative glaucoma (PEXG-SLT group). The PEXG-SLT patients underwent a trabeculectomy for uncontrolled IOP in the eye that showed increased IOP despite the maximum drug treatment with β-blockers and dorzolamide eye drops and after ineffective selective laser trabeculoplasty (SLT). The control group consisted of 15 subjects with cataracts. Aqueous humor was aspirated during surgery from patients with PEXG-C, PEXG-SLT and from matched control patients with cataracts during cataract surgery or trabeculectomy. The concentrations of MMP-2 and TIMP-2 in the aqueous humor were assessed with commercially available ELISA kits.</p> <p>Results</p> <p>In PEXG-SLT group in the first 10 days after SLT treatment a significant reduction in IOP was observed: 25.8 ± 1.9 vs 18.1.0 ± 1.4 mm/Hg (p < 0.001), but after a mean time of 31.5 ± 7.6 days IOP increased and returned to pretreatment levels: 25.4 ± 1.6 mm/Hg (p < 0.591). Therefore a trabeculectomy was considered necessary.</p> <p>The MMP-2 in PEXG-C was 57.77 ± 9.25 μg/ml and in PEXG-SLT was 58.52 ± 9.66 μg/ml (p < 0.066). TIMP-2 was 105.19 ± 28.53 μg/ml in PEXG-C and 105.96 ± 27.65 μg/ml in PEXG-SLT (p < 0.202). The MMP-2/TIMP-2 ratio in the normal subjects was 1.11 ± 0.44. This ratio increase to 1.88 ± 0.65 in PEXG-C (p < 0.001) and to 1.87 ± 0.64 in PEXG-SLT (p < 0.001). There was no statistically significant difference between the PEXG-C and PEXG-SLT ratios (p < 0.671).</p> <p>Conclusion</p> <p>This case series suggest that IOP elevation after SLT can be a serious adverse event in some PEXG patients. The IOP increase in these cases would be correlated to the failure to decrease the TIMP-2/MMP-2 ratio.</p> <p>Trial registration</p> <p>Current Controlled Trials <b>ISRCTN79745214</b></p

Polyamine Sharing between Tubulin Dimers Favours Microtubule Nucleation and Elongation via Facilitated Diffusion

We suggest for the first time that the action of multivalent cations on microtubule dynamics can result from facilitated diffusion of GTP-tubulin to the microtubule ends. Facilitated diffusion can promote microtubule assembly, because, upon encountering a growing nucleus or the microtubule wall, random GTP-tubulin sliding on their surfaces will increase the probability of association to the target sites (nucleation sites or MT ends). This is an original explanation for understanding the apparent discrepancy between the high rate of microtubule elongation and the low rate of tubulin association at the microtubule ends in the viscous cytoplasm. The mechanism of facilitated diffusion requires an attraction force between two tubulins, which can result from the sharing of multivalent counterions. Natural polyamines (putrescine, spermidine, and spermine) are present in all living cells and are potent agents to trigger tubulin self-attraction. By using an analytical model, we analyze the implication of facilitated diffusion mediated by polyamines on nucleation and elongation of microtubules. In vitro experiments using pure tubulin indicate that the promotion of microtubule assembly by polyamines is typical of facilitated diffusion. The results presented here show that polyamines can be of particular importance for the regulation of the microtubule network in vivo and provide the basis for further investigations into the effects of facilitated diffusion on cytoskeleton dynamics