Global stability in time-delayed single-species dynamics

Criteria are established for three classes of models of single-species dynamics with a single discrete delay to have a globally asymptotically stable positive equilibrium independent of the length of delay. Research partially supported by the NSERC of Canada, grant No. A4823. Research was carried out while the author was a distinguished visitor at the University of Alberta.     

Harmless delays in model systems

An autonomous system of two differential equations with an asymptotically stable steady state is considered. It is shown that there exists a class of time delays which preserves the stability of such a steady state. The charactristic return time (or decay rate) for the solutions to approach the steady state is estimated using the variational system for the perturbations.     

Pursuit-evasion wave trains in prey-predator systems with diffusionally coupled delays

The Lotka-Volterra system of prey-predator equations is considered with a special type of continuous time delay. In the case of equal diffusion coefficients Hopf’s bifurcation technique is used to show the existence of travelling wave train solutions for the prey-predator system.     

Identification and SAR of a new series of thieno[3,2-d]pyrimidines as Tpl2 kinase inhibitors

We report here the synthesis and SAR of a new series of thieno[3,2-d]pyrimidines as potent Tpl2 kinase inhibitors. The proposed binding mode suggests the potential flipped binding mode depending on the substitution. Biacore studies show evidence of binding of these molecules to the protein kinase. The kinome inhibition profile of these molecules suggests good selectivity.     

Age-specific coexistence in two-species competition

Sufficient conditions are obtained for the existence and linear stability of stationary age distributions in a two-species competition model with age-dependent mortality and fertility functions.     

Non-hinge-binding pyrazolo[1,5-a]pyrimidines as potent B-Raf kinase inhibitors

As part of our research effort to discover B-Raf kinase inhibitors, we prepared a series of C-3 substituted N-(3-(pyrazolo[1,5-a]pyrimidin-7-yl)phenyl)-3-(trifluoromethyl)benzamides. X-ray crystallography studies revealed that one of the more potent inhibitors (10n) bound to B-Raf kinase without forming a hinge-binding hydrogen bond. With basic amine residues appended to C-3 aryl residues, cellular activity and solubility were enhanced over previously described compounds of this class.     

Limit cycles in periodically perturbed population systems

A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.     

Persistence in periodic and almost periodic Lotka-Volterra systems

It is shown that a strongly self-regulating (or resource limited) Lotka-Volterra population system can persist in a periodic or almost periodic environment if and only if the system tracks the environmental variations.     

AuBr3 mediated glycosidations: synthesis of tetrasaccharide motif of the Leishmania donovani lipophosphoglycan

Tetrasaccharide cap present in lipophosphoglycan of the Leishmania donovani responsible for visceral Leishmaniaisis is synthesized as a fully protected propargyl glycoside. AuBr(3) mediated selective glycosylation of propargyl 1,2-orthoester in the presence of propargyl glycoside is employed as a key step to obtain propargyl containing oligomers. Further, propargyl tetrasaccharide is connected with a long chain hydrocarbon containing azidothiol functionality situated at two terminal ends via 'click' reaction.     

Design and synthesis of 2,3,4,9-tetrahydro-1H-carbazole and 1,2,3,4-tetrahydro-cyclopenta[b]indole derivatives as non-nucleoside inhibitors of hepatitis C virus NS5B RNA-dependent RNA polymerase

A novel class of HCV NS5B RNA dependent RNA polymerase inhibitors containing 2,3,4,9-tetrahydro-1H-carbazole and 1,2,3,4-tetrahydro-cyclopenta[b]indole scaffolds were designed and synthesized. Optimization of the aromatic region showed preference for 5,8-disubstitution pattern in both the scaffolds examined while favoring the n-propyl moiety for the C-1 position. 1,2,3,4-tetrahydro-cyclopenta[b]indole scaffold was slightly more potent than the corresponding 2,3,4,9-tetrahydro-1H-carbazole and analogue 36 displayed an IC50 of 550 nM against HCV NS5B enzyme.