On the variational limits of lattice energies on prestrained elastic bodies

We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric $G$, assigned on the continuum reference configuration $\Omega$. When the mesh size of the discrete lattice in $\Omega$ goes to zero, we obtain the variational bounds on the limiting (in the sense of $\Gamma$-limit) energy. In case of the nearest-neighbour and next-to-nearest-neibghour interactions, we derive a precise asymptotic formula, and compare it with the non-Euclidean model energy relative to $G$

Dysregulations of sonic hedgehog signaling in MED12-related X-linked intellectual disability disorders

BACKGROUND:Mutations in mediator of RNA polymerase II transcription subunit 12 homolog (MED12, OMIM 300188) cause X-linked intellectual disability (XLID) disorders including FG, Lujan, and Ohdo syndromes. The Gli3-dependent Sonic Hedgehog (SHH) signaling pathway has been implicated in the original FG syndrome and Lujan syndrome. How are SHH-signaling defects related to the complex clinical phenotype of MED12-associated XLID syndromes are not fully understood. METHODS:Quantitative RT-PCR was used to study expression levels of three SHH-signaling genes in lymophoblast cell lines carrying four MED12 mutations from four unrelated XLID families. Genotype and phenotype correlation studies were performed on these mutations. RESULTS:Three newly identified and one novel MED12 mutations in six affected males from four unrelated XLID families were studied. Three mutations (c.2692A>G; p.N898D, c.3640C>T; p.R1214C, and c.3884G>A; p.R1295H) are located in the LS domain and one (c.617G>A; p.R206Q) is in the L domain of MED12. These mutations involve highly conserved amino acid residues and segregate with ID and related congenital malformations in respective probands families. Patients with the LS-domain mutations share many features of FG syndrome and some features of Lujan syndrome. The patient with the L-domain mutation presented with ID and predominant neuropsychiatric features but little dysmorphic features of either FG or Lujan syndrome. Transcript levels of three Gli3-dependent SHH-signaling genes, CREB5, BMP4, and NEUROG2, were determined by quantitative RT-PCR and found to be significantly elevated in lymphoblasts from patients with three mutations in the MED12-LS domain. CONCLUSIONS:These results support a critical role of MED12 in regulating Gli3-dependent SHH signaling and in developing ID and related congenital malformations in XLID syndromes. Differences in the expression profile of SHH-signaling genes potentially contribute to variability in clinical phenotypes in patients with MED12-related XLID disorders.Siddharth Srivastava, Tejasvi Niranjan, Melanie M. May, Patrick Tarpey, William Allen ... Jozef Gecz ... et al