Asymptotic Behavior of Solutions to Nonlinear Fractional Differential Equations

It is known that, under certain conditions, solutions of some ordinary differential equations of first, second or even higher order are asymptotic to polynomials as time goes to infinity. We generalize and extend some of the existing results to differential equations of non-integer order. Reasonable conditions and appropriate underlying spaces are determined ensuring that solutions of fractional differential equations with nonlinear right hand sides approach power type functions as time goes to infinity. The case of fractional differential problems with fractional damping is also considered. Our results are obtained by using generalized versions of GronwallBellman inequality and appropriate desingularization techniques

Trypanosoma cruzi CYP51 Inhibitor Derived from a Mycobacterium tuberculosis Screen Hit

Enzyme sterol 14α-demethylase (CYP51) is a well-established target for anti-fungal therapy and is a prospective target for Chagas' disease therapy. We previously identified a chemical scaffold capable of delivering a variety of chemical structures into the CYP51 active site. In this work the binding modes of several second generation compounds carrying this scaffold were determined in high-resolution co-crystal structures with CYP51 of Mycobacterium tuberculosis. Subsequent assays against CYP51 in Trypanosoma cruzi, the agent of Chagas' disease, demonstrated that two of the compounds bound tightly to the enzyme. Both were tested for inhibitory effects against T. cruzi and the related protozoan parasite Trypanosoma brucei. One of the compounds had potent, selective anti–T. cruzi activity in infected mouse macrophages. This compound is currently being evaluated in animal models of Chagas' disease. Discrimination between T. cruzi and T. brucei CYP51 by the inhibitor was largely based on the variability of a single amino acid residue at a critical position in the active site. Our work is aimed at rational design of potent and highly selective CYP51 inhibitors with potential to become therapeutic drugs. Drug selectivity to prevent host–pathogen cross-reactivity is pharmacologically important, because CYP51 is present in human host

Structural Characterization of CYP51 from Trypanosoma cruzi and Trypanosoma brucei Bound to the Antifungal Drugs Posaconazole and Fluconazole

Chagas Disease is caused by kinetoplastid protozoa Trypanosoma cruzi, whose sterols resemble those of fungi, in both composition and biosynthetic pathway. Azole inhibitors of sterol 14α-demethylase (CYP51), such as fluconazole, itraconazole, voriconazole, and posaconazole, successfully treat fungal infections in humans. Efforts have been made to translate anti-fungal azoles into a second-use application for Chagas Disease. Ravuconazole and posaconazole have been recently proposed as candidates for clinical trials with Chagas Disease patients. However, the widespread use of posaconazole for long-term treatment of chronic infections may be limited by hepatic and renal toxicity, a requirement for simultaneous intake of a fatty meal or nutritional supplement to enhance absorption, and cost. To aid our search for structurally and synthetically simple CYP51 inhibitors, we have determined the crystal structures of the CYP51 targets in T. cruzi and T. brucei, both bound to the anti-fungal drugs fluconazole or posaconazole. The structures provide a basis for a design of new drugs targeting Chagas Disease, and also make it possible to model the active site characteristics of the highly homologous Leishmania CYP51. This work provides a foundation for rational synthesis of new therapeutic agents targeting the three kinetoplastid parasites

Efficiency of Beam-Column Joint Strengthened by FRP Laminates

International audienceThe recent earthquakes have shown that the vulnerability and the defects of the concrete joints in beam- column framed structures were the main causes for many building collapses. Such vulnerability and defects are in general the consequences of many factors. External strengthening with composite materials represents an alternative and a sound and efficient technique to improve the performances and aptitude to withstand seismic action. However, while the use of such strengthening technique offers many advantages, it has some disadvantages, particularly a remarkable loss of ductility. The present study examines the effects of an external strengthening of reinforced concrete beam-column joints against cyclic loading using CFRP laminates and GFRP sheet. The experimental program is constituted of three beam-column reinforced concrete joints at a scale of one to three (1/3) tested under the effect of a prestressing axial load acting over the column. The beams were subjected at their ends to a reverse cyclic loading under displacement control to simulate a seismic action. Strain and cracking fields were monitored with the help a digital recording camera. Following the analysis of the results, a comparison was made concerning the performances in terms of ductility, strength and mode of failure of the different strengthening solutions

Asymptotic behavior of solutions to nonlinear initial-value fractional differential problems

We study the boundedness and asymptotic behavior of solutions for a class of nonlinear fractional differential equations. These equations involve two Riemann-Liouville fractional derivatives of different orders. We determine fairly large classes of nonlinearities and appropriate underlying spaces where solutions are bounded, exist globally and decay to zero as a power type function. Our results are obtained by using generalized versions of Gronwall-Bellman inequality, appropriate regularization techniques and several properties of fractional derivatives. Three examples are given to illustrate our results

Non-existence of global solutions for a differential equation involving Hilfer fractional derivative

We consider a basic fractional differential inequality with a fractional derivative named after Hilfer and a polynomial source. A non-existence of global solutions result is proved in an appropriate space and the critical exponent is shown to be optimal