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The author adopts previously developed methods of quantum propagation which use trajectory-guided sets of Gaussian Coherent States for the use with SU(2) Coherent States. Motivated by recent experiments, the author applies the technique to the simulation of quantum dynamics in a chain of coupled qubits. Because of the short time dynamics can be reproduced on a selected small basis set of Coupled SU(2) Coherent States. To recover long-time dynamics observed in the experiment propagation on a small localised basis is combined with projection on an optimised static basis.

We prove both analytically and numerically that the total angular momentum of a molecular system undergoing adiabatic Born-Oppenheimer dynamics is conserved only when pseudo-magnetic Berry forces are taken into account. This finding sheds light on the nature of Berry forces for molecular systems with spin-orbit coupling and highlights how ab initio Born-Oppenheimer molecular dynamics simulations can successfully capture the entanglement of spin and nuclear degrees of freedom as modulated by electronic interactions.

BACKGROUND: Heterogeneity of gene expression in Glioblastoma (GBM) has been recently recognised as a key feature involved in therapy resistance with invasive cells remaining after surgery and displaying unique molecular features. The dysregulation of small non-coding RNAs known as microRNAs (miRNAs) can disrupt gene regulatory networks and contribute to GBM development. However, the intra-tumour heterogeneity of miRNA expression in GBM has not yet been investigated. MATERIAL AND METHODS: Global miRNA expression profiling was performed in 45 GBM surgical specimens sampled from the tumour necrotic core, proliferative rim and the invasive margin. Gain-of-function studies were conducted using transfection of selected mature miRNAs into GBM cell lines. Global metabolomic profiling by liquid chromatography coupled with electrospray mass spectrometry (LC-ESI-MS) and gene expression assays were used to identify molecular targets regulated by miRNAs in GBM cells. Transwell assays were performed to examine the migration and invasion effects of inhibiting targets expression. Evaluation of targets expression in tumour tissue samples was performed by qRT-PCR, flow cytometry and immunohistochemical analysis. RESULTS: We identified two significantly upregulated miRNAs in the invasive margin compared to the core and the rim of the tumour. Integrated metabolomic and gene expression analysis revealed that these miRNAs may act synergistically to target key enzymes involved in fatty acid oxidation (ACOX1 and CPT2) and lipoprotein uptake and secretion (LDLR). ACOX1, CPT2 and LDLR were found to be expressed at lower levels in the core and the rim relative to the tumour invasive margin. The pharmacological inhibition of CPT2 and LDLR resulted in a significant reduction in GBM cell invasion. CONCLUSION: Our finding indicates that lipid metabolism may present a possible vulnerability of GBM invasive margin. Understanding the function of miRNAs in regulating lipid homeostasis in GBM may provide novel avenues for GBM therapy.