Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.

Biochemical studies of postsynaptic density signaling proteins with a focus on synaptic GTPase activating protein and PDZ domains

Memory storage in the brain involves adjustment of the strength of existing synapses and formation of new neural networks. A key process underlying memory formation is synaptic plasticity, the ability of excitatory synapses to strengthen or weaken their connections in response to patterns of activity between their connected neurons. Synaptic plasticity is governed by the precise pattern of Ca²⁺ influx through postsynaptic N-methyl-D-aspartate-type glutamate receptors (NMDARs), which can lead to the activation of the small GTPases Ras and Rap. Differential activation of Ras and Rap acts to modulate synaptic strength by promoting the insertion or removal of 2-amino-3-(3-hydroxy-5-methyl-isoxazol-4-yl)propanoic acid receptors (AMPARs) from the synapse. Synaptic GTPase activating protein (synGAP) regulates AMPAR levels by catalyzing the inactivation of GTP-bound (active) Ras or Rap. synGAP is positioned in close proximity to the cytoplasmic tail regions of the NMDAR through its association with the PDZ domains of PSD-95. SynGAP’s activity is regulated by the prominent postsynaptic protein kinase, Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) and cyclin-dependent kinase 5 (CDK5), a known binding partner of CaMKII. Modulation of synGAP’s activity by phosphorylation may alter the ratio of active Ras to Rap in spines, thus pushing the spine towards the insertion or removal of AMPARs, subsequently strengthening or weakening the synapse. To date, all biochemical studies of the regulation of synGAP activity by protein kinases have utilized impure preparations of membrane bound synGAP. Here we have clarified the effects of phosphorylation of synGAP on its Ras and Rap GAP activities by preparing and utilizing purified, soluble recombinant synGAP, Ras, Rap, CaMKII, CDK5, PLK2, and CaM. Using mass spectrometry, we have confirmed the presence of previously identified CaMKII and CDK5 sites in synGAP, and have identified novel sites of phosphorylation by CaMKII, CDK5, and PLK2. We have shown that the net effect of phosphorylation of synGAP by CaMKII, CDK5, and PLK2 is an increase in its GAP activity toward HRas and Rap1. In contrast, there is no effect on its GAP activity toward Rap2. Additionally, by assaying the GAP activity of phosphomimetic synGAP mutants, we have been able to hypothesize the effects of CDK5 phosphorylation at specific sites in synGAP. In the course of this work, we also found, unexpectedly, that synGAP is itself a Ca²⁺/CaM binding protein. While Ca²⁺/CaM binding does not directly affect synGAP activity, it causes a conformational change in synGAP that increases the rate of its phosphorylation and exposes additional phosphorylation sites that are inaccessible in the absence of Ca²⁺/CaM.

The postsynaptic density (PSD) is an electron-dense region in excitatory postsynaptic neurons that contains a high concentration of glutamate receptors, cytoskeletal proteins, and associated signaling enzymes. Within the PSD, three major classes of scaffolding molecules function to organize signaling enzymes and glutamate receptors. PDZ domains present in the Shank and PSD-95 scaffolds families serve to physically link AMPARs and NMDARs to signaling molecules in the PSD. Because of the specificity and high affinity of PDZ domains for their ligands, I reasoned that these interacting pairs could provide the core components of an affinity chromatography system, including affinity resins, affinity tags, and elution agents. I show that affinity columns containing the PDZ domains of PSD-95 can be used to purify active PDZ domain-binding proteins to very high purity in a single step. Five heterologously expressed neuronal proteins containing endogenous PDZ domain ligands (NMDAR GluN2B subunit Tail, synGAP, neuronal nitric oxide synthase PDZ domain, cysteine rich interactor of PDZ three and cypin) were purified using PDZ domain resin, with synthetic peptides having the sequences of cognate PDZ domain ligands used as elution agents. I also show that conjugation of PDZ domain-related affinity tags to Proteins Of Interest (POIs) that do not contain endogenous PDZ domains or ligands does not alter protein activity and enables purification of the POIs on PDZ domain-related affinity resins.