A finite element method for second order nonvariational elliptic problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

Generation of anti-complement "prodrugs": cleavable reagents for specific delivery of complement regulators to disease sites

Expression of biologically active molecules as fusion proteins with antibody Fc can substantially extend the plasma half-life of the active agent but may also influence function. We have previously generated a number of fusion proteins comprising a complement regulator coupled to Fc and shown that the hybrid molecule has a long plasma half-life and retains biological activity. However, several of the fusion proteins generated had substantially reduced biological activity when compared with the native regulator or regulator released from the Fc following papain cleavage. We have taken advantage of this finding to engineer a prodrug with low complement regulatory activity that is cleaved at sites of inflammation to release active regulator. Two model prodrugs, comprising, respectively, the four short consensus repeats of human decay accelerating factor (CD55) linked to IgG4 Fc and the three NH2-terminal short consensus repeats of human decay accelerating factor linked to IgG2 Fc have been developed. In each, specific cleavage sites for matrix metalloproteinases and/or aggrecanases have been incorporated between the complement regulator and the Fc. These prodrugs have markedly decreased complement inhibitory activity when compared with the parent regulator in vitro. Exposure of the prodrugs to the relevant enzymes, either purified, or in supernatants of cytokine-stimulated chondrocytes or in synovial fluid, efficiently cleaved the prodrug, releasing active regulator. Such agents, having negligible systemic effects but active at sites of inflammation, represent a paradigm for the next generation of anti-C therapeutics.

Discovery of three polymorphs of 7-fluoroisatin reveals challenges in using computational crystal structure prediction as a complement to experimental screening

A combined computational and experimental polymorph search was undertaken to establish the crystal forms of 7-fluoroisatin, a simple molecule with no reported crystal structures, to evaluate the value of crystal structure prediction studies as an aid to solid form discovery. Three polymorphs were found in a manual crystallisation screen, as well as two solvates. Form I ( P2(1)/c, Z0 1), found from the majority of solvent evaporation experiments, corresponded to the most stable form in the computational search of Z0 1 structures. Form III ( P21/ a, Z0 2) is probably a metastable form, which was only found concomitantly with form I, and has the same dimeric R2 2( 8) hydrogen bonding motif as form I and the majority of the computed low energy structures. However, the most thermodynamically stable polymorph, form II ( P1 , Z0 2), has an expanded four molecule R 4 4( 18) hydrogen bonding motif, which could not have been found within the routine computational study. The computed relative energies of the three forms are not in accord with experimental results. Thus, the experimental finding of three crystalline polymorphs of 7- fluoroisatin illustrates the many challenges for computational screening to be a tool for the experimental crystal engineer, in contrast to the results for an analogous investigation of 5- fluoroisatin.