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- SourceAvailable from: Jian S Dai[Show abstract] [Hide abstract]
ABSTRACT: This paper reviews the Euler–Rodrigues formula in the axis–angle representation of rotations, studies its variations and derivations in different mathematical forms as vectors, quaternions and Lie groups and investigates their intrinsic connections. The Euler–Rodrigues formula in the Taylor series expansion is presented and its use as an exponential map of Lie algebras is discussed particularly with a non-normalized vector. The connection between Euler–Rodrigues parameters and the Euler–Rodrigues formula is then demonstrated through quaternion conjugation and the equivalence between quaternion conjugation and an adjoint action of the Lie group is subsequently presented. The paper provides a rich reference for the Euler–Rodrigues formula, the variations and their connections and for their use in rigid body kinematics, dynamics and computer graphics.Mechanism and Machine Theory 10/2015; 92. DOI:10.1016/j.mechmachtheory.2015.03.004
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ABSTRACT: The cell membrane is a highly complex designed material with remarkable physicochemical properties; comprised mainly of lipid moieties, it is capable of self-assembling, changing morphology, housing a range of distinct proteins, and withstanding electrical, chemical and mechanical perturbations. All of these fundamental cellular functions occurring within a 5nm thick film is an astonishing feat of engineering, made possible due to the interplay of a variety of intermolecular forces. Elucidating how the interactions within the chemically distinct partners influence the nanomechanical properties of the membrane is essential to gain a comprehensive understanding of a wide-variety of both force-triggered and force-sensing mechanisms that dictate essential cellular processes.Current opinion in chemical biology 10/2015; 29:87-93. DOI:10.1016/j.cbpa.2015.09.019
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ABSTRACT: Leishmania infantum, causative agent of visceral leishmaniasis in humans, illustrates a complex lifecycle pertaining to two extreme environments, namely, the gut of the sandfly vector and human macrophages. Leishmania is capable of dynamically adapting and tactically switching between these critically hostile situations. The possible metabolic routes ventured by the parasite to achieve this exceptional adaptation to its varying environments are still poorly understood. In this study, we present an extensively reconstructed energy metabolism network of Leishmania infantum as an attempt to identify certain strategic metabolic routes preferred by the parasite to optimize its survival in such dynamic environments. The reconstructed network consists of 142 genes encoding for enzymes performing 237 reactions distributed across five distinct model compartments. We annotated the subcellular locations of different enzymes and their reactions on the basis of strong literature evidence and sequence-based detection of cellular localization signal within a protein sequence. To explore the diverse features of parasite metabolism the metabolic network was implemented and analyzed as a constraint-based model. Using a systems-based approach, we also put forth an extensive set of lethal reaction knockouts; some of which were validated using published data on Leishmania species. Performing a robustness analysis, the model was rigorously validated and tested for the secretion of overflow metabolites specific to Leishmania under varying extracellular oxygen uptake rate. Further, the fate of important non-essential amino acids in L. infantum metabolism was investigated. Stage-specific scenarios of L. infantum energy metabolism were incorporated in the model and key metabolic differences were outlined. Analysis of the model revealed the essentiality of glucose uptake, succinate fermentation, glutamate biosynthesis and an active TCA cycle as driving forces for parasite energy metabolism and its optimal growth. Finally, through our in silico knockout analysis, we could identify possible therapeutic targets that provide experimentally testable hypotheses.PLoS ONE 10/2015; 10(9). DOI:10.1371/journal.pone.0137976
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