A biophysical framework for double-drugging kinases.

Orthosteric inhibition of kinases has been challenging due to the conserved active site architecture of kinases and emergence of resistance mutants. Simultaneous inhibition of distant orthosteric and allosteric sites, which we refer to as "double-drugging", has recently been shown to be effective in overcoming drug resistance. However, detailed biophysical characterization of the cooperative nature between orthosteric and allosteric modulators has not been undertaken. Here, we provide a quantitative framework for double-drugging of kinases employing isothermal titration calorimetry, Förster resonance energy transfer, coupled-enzyme assays, and X-ray crystallography. We discern positive and negative cooperativity for Aurora A kinase (AurA) and Abelson kinase (Abl) with different combinations of orthosteric and allosteric modulators. We find that a conformational equilibrium shift is the main principle governing this cooperative effect. Notably, for both kinases, we find a synergistic decrease of the required orthosteric and allosteric drug dosages when used in combination to inhibit kinase activities to clinically relevant inhibition levels. X-ray crystal structures of the doubledrugged kinase complexes reveal the molecular principles underlying the cooperative nature of double-drugging AurA and Abl with orthosteric and allosteric inhibitors. Finally, we observe the first fully-closed conformation of Abl when bound to a pair of positively cooperative orthosteric and allosteric modulators, shedding light onto the puzzling abnormality of previously solved closed Abl structures. Collectively, our data provide mechanistic and structural insights into rational design and evaluation of doubledrugging strategies.

Kinase dynamics. Using ancient protein kinases to unravel a modern cancer drug's mechanism.

Macromolecular function is rooted in energy landscapes, where sequence determines not a single structure but an ensemble of conformations. Hence, evolution modifies a protein's function by altering its energy landscape. Here, we recreate the evolutionary pathway between two modern human oncogenes, Src and Abl, by reconstructing their common ancestors. Our evolutionary reconstruction combined with x-ray structures of the common ancestor and pre-steady-state kinetics reveals a detailed atomistic mechanism for selectivity of the successful cancer drug Gleevec. Gleevec affinity is gained during the evolutionary trajectory toward Abl and lost toward Src, primarily by shifting an induced-fit equilibrium that is also disrupted in the clinical T315I resistance mutation. This work reveals the mechanism of Gleevec specificity while offering insights into how energy landscapes evolve.

Reflectivity of cholesteric liquid crystals with spatially varying pitch.

Solids with spatially varying photonic structure offer gaps to light of a wider range of frequencies than do simple photonic systems. We solve numerically the field distribution in a cholesteric with a linearly varying inverse pitch (helical wavevector) using equations we derive for the general case. The simple idea that the position where the Bragg condition is locally satisfied is where reflection takes place is only true in part. Here, reflection is due to a region where the waves are forced to become evanescent, and the rate of variation of structure determines over which distance the waves decay and therefore how complete reflection is. The approximate local Bragg-de Vries schemes are shown to break down in detail at the edges of the gap, and an analytical estimate is given for the transmission coefficient.

Uniaxial and biaxial soft deformations of nematic elastomers.

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this nonclassical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the polar decomposition theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors and that of finding explicit forms for soft deformations (the approach of Olmsted) are discussed in this context.

Networks of helix-forming polymers.

Biological molecules can form hydrogen bonds between nearby residues, leading to helical secondary structures. The associated reduction of configurational entropy leads to a temperature dependence of this effect: the helix-coil transition. Since the formation of helices implies a dramatic shortening of the polymer dimensions, an externally imposed end-to-end distance R affects the equilibrium helical fraction of the polymer and the resulting force-extension curves show anomalous plateau regimes. In this article, we investigate the behaviour of a crosslinked network of such helicogenic molecules, particularly focusing on the coupling of the (average) helical content present in a network to the externally imposed strain. We show that both elongation and compression can lead to an increase in helical domains under appropriate conditions.