On approximation theorems for controllability of non-linear parabolic problems

^** Email: anil{at}math.iitb.ac.in^*** Email: mcj{at}math.iitb.ac.in^**** Email: akp{at}math.iitb.ac.in In this paper, we consider the following control system governedby the non-linear parabolic differential equation of the form: [graphic: see PDF] where A is a linear operator with dense domain and f(t, y)is a non-linear function. We have proved that under Lipschitzcontinuity assumption on the non-linear function f(t, y), theset of admissible controls is non-empty. The optimal pair (u^*,y^*) is then obtained as the limit of the optimal pair sequence{(u_n^*, y_n^*)}, where u_n^* is a minimizer of the unconstrainedproblem involving a penalty function arising from the controllabilityconstraint and y_n^* is the solution of the parabolic non-linearsystem defined above. Subsequently, we give approximation theoremswhich guarantee the convergence of the numerical schemes tooptimal pair sequence. We also present numerical experimentwhich shows the applicability of our result.     

Temperature-dependent phase behavior of polyelectrolyte-mixed micelle systems

The effect of temperature on the phase behavior of a polycation-anionic/nonionic mixed micelle system, poly(dimethyldiallylammonium chloride)-sodium dodecylsulfate/Triton X-100, was studied over a wide range of surfactant compositions, ionic strengths, and polycation molecular weights using turbidimetry and dynamic light scattering. Soluble complexes become biphasic upon heating through either liquid-liquid (coacervation) or liquid-solid (precipitation) separation. The biphasic boundary comprises two regions: a coacervate domain exhibiting a lower critical solution temperature and a second superimposed domain in which either solids or very dense and viscous fluids are formed upon heating. The position of the first region is symmetrically centered around conditions corresponding to charge neutralization of complexes and their aggregates at incipient phase separation. The second region, observed at high micelle charge, corresponds to the collapse of polycation onto micelle surfaces and expulsion of counterions and can produce either dense coacervate or precipitate. The two regions exhibit different dependences on ionic strength, polyelectrolyte molecular weight, and concentration, from which inferences about the mechanisms of phase separation may be drawn. Preliminary observations of the dense liquid phases isolated after coacervation disclose a number of interesting optical and rheological properties, possibly arising from shear-induced phase separation.     

Boltzmann statistics rotational-echo double-resonance analysis

A new approach to rotational-echo double-resonance (REDOR) data analysis, analogous to Boltzmann maximum entropy statistics, is reported. This Boltzmann statistics REDOR (BS-REDOR) approach is useful for reconstructing an unbiased internuclear distance distribution for multiple internuclear distances from experimentally limited REDOR data sets on isolated spin pairs. The analysis is characterized by exploring reconstructions on model data and applied to both [1-(13)C,15N]-glycine and a long intramolecular distance in Abeta (16-22) peptide nanotubes. The approach also provides insight into the minimal number of REDOR data points required to allow faithful determination of dipolar couplings in systems with multiple internuclear distances.     

Catalytic residues are shared between two pseudosubunits of the dehydratase domain of the animal fatty acid synthase

Expression, characterization, and mutagenesis of a series of N-terminal fragments of an animal fatty acid synthase, containing the beta-ketoacyl synthase, acyl transferase, and dehydratase domains, demonstrate that the dehydratase domain consists of two pseudosubunits, derived from contiguous regions of the same polypeptide, in which a single active site is formed by the cooperation of the catalytic histidine 878 residue of the first pseudosubunit with aspartate 1032 of the second pseudosubunit. Mutagenesis and modeling studies revealed an essential role for glutamine 1036 in anchoring the position of the catalytic aspartate. These findings establish that sequence elements previously assigned to a central structural core region of the type I fatty acid synthases and some modular polyketide synthase counterparts play an essential catalytic role as part of the dehydratase domain.     

Spectral, IR and magnetic studies of Mn(II), Co(II), Ni(II) and Cu(II) complexes with pyrrole-2-carboxyaldehyde thiosemicarbazone (L)

Mn(II), Co(II), Ni(II) and Cu(II) complexes are synthesized with thiosemicarbazone (L) derived from pyrrole-2-carboxyaldehyde. These complexes are characterized by elemental analysis, molar conductance, magnetic susceptibility measurement, mass, IR, electronic and EPR spectral studies. The molar conductance measurement of the complexes in DMSO indicates that the complexes are non-electrolyte except Co(L)2(NO3)2 and Ni(L)2(NO3)2 complexes which are 1:2 electrolyte. All the complexes are of high-spin type. On the basis of spectral studies an octahedral geometry may be assigned for Mn(II), Co(II) and Ni(II) complexes except Co(L)2(NO3)2 and Ni(L)2(NO3)2 which are of tetrahedral geometry. A tetragonal geometry may be suggested for Cu(II) complexes.     

A water-soluble fluorescent fluoride ion probe based on Alizarin Red S-Al(III) complex

A new water-soluble fluorescent fluoride ion signaling system has been developed based on the ligand exchange mechanism in aqueous medium. This procedure is based on the exchange of two Alizarin Red S (ARS) molecules coordinated to Al(III) by fluoride ion without interference from other common anions. The binary complex of ARS with Al(III) provides a sensitive signaling system for fluoride ion in the concentration range from 5x10(-6) to 3x10(-4) M. The ligand exchange reaction of ARS-Al(III) complex with fluoride ion has been investigated by UV-vis and fluorescence spectroscopies combined with the AM1 semi-empirical quantum chemical calculations. The pale orange fluorescence (lambdamax=575 nm) exhibited by the complex upon excitation at 435 nm decreases in intensity with fluoride addition with a detection limit of 0.1 mg L-1.     

First triazole-bridged unsymmetrical porphyrin dyad via click chemistry

Click chemistry has been successfully applied in the synthesis of the first example of a triazole-bridged porphyrin dyad containing N(2)S(2) porphyrin and N(4) or ZnN(4) porphyrin subunits, and fluorescence study indicated a possibility of singlet-singlet energy transfer from the N(4) or ZnN(4) porphyrin subunit to the N(20S(2) porphyrin subunit.     

Effect of base stacking on the acid-base properties of the adenine cation radical [A*+] in solution: ESR and DFT studies

In this study, the acid-base properties of the adenine cation radical are investigated by means of experiment and theory. Adenine cation radical (A*(+)) is produced by one-electron oxidation of dAdo and of the stacked DNA-oligomer (dA)6 by Cl2*(-) in aqueous glass (7.5 M LiCl in H2O and in D2O) and investigated by ESR spectroscopy. Theoretical calculations and deuterium substitution at C8-H and N6-H in dAdo aid in our assignments of structure. We find the pKa value of A*(+) in this system to be ca. 8 at 150 K in seeming contradiction to the accepted value of < or = 1 at ambient temperature. However, upon thermal annealing to > or = 160 K, complete deprotonation of A*(+) occurs in dAdo in these glassy systems even at pH ca. 3. A*(+) found in (dA)6 at 150 K also deprotonates on thermal annealing. The stability of A*(+) at 150 K in these systems is attributed to charge delocalization between stacked bases. Theoretical calculations at various levels (DFT B3LYP/6-31G*, MPWB95, and HF-MP2) predict binding energies for the adenine stacked dimer cation radical of 12 to 16 kcal/mol. Further DFT B3LYP/6-31G* calculations predict that, in aqueous solution, monomeric A*(+) should deprotonate spontaneously (a predicted pKa of ca. -0.3 for A*(+)). However, the charge resonance stabilized dimer AA*(+) is predicted to result in a significant barrier to deprotonation and a calculated pKa of ca. 7 for the AA*(+) dimer which is 7 pH units higher than the monomer. These theoretical and experimental results suggest that A*(+) isolated in solution and A*(+) in adenine stacks have highly differing acid-base properties resulting from the stabilization induced by hole delocalization within adenine stacks.     

Facial symmetry in protein self-assembly

Amyloids are self-assembled protein architectures implicated in dozens of misfolding diseases. These assemblies appear to emerge through a "selection" of specific conformational "strains" which nucleate and propagate within cells to cause disease. The short Abeta(16-22) peptide, which includes the central core of the Alzheimer's disease Abeta peptide, generates an amyloid fiber which is morphologically indistinguishable from the full-length peptide fiber, but it can also form other morphologies under distinct conditions. Here we combine spectroscopic and microscopy analyses that reveal the subtle atomic-level differences that dictate assembly of two conformationally pure Abeta(16-22) assemblies, amyloid fibers and nanotubes, and define the minimal repeating unit for each assembly.