| Summary: | 碩士 === 國立清華大學 === 化學系 === 104 === I. Monodisperse lipid nanodisc provides bacteriorhodopsin (bR), a light-driven proton pump membrane protein, excellent aqueous dispersibility and native-mimic lipid bilayer environment. To study the lipid-composition dependence of the photo-cycle kinetics of bR, the monomeric bR was embedded in nanodiscs composed of different ratios of negatively-charged lipids (DMPG, DOPG) to zwitterionic lipids (DMPC, DOPC). The steady-state absorption spectra of light-adapted monomeric bR in nanodiscs composed of different lipid ratios exhibited the conservation of the tertiary structure of embedded bR and the ion-exchange chromatography showed increment on negative surface charge as the content of DOPG or DMPG increased. By utilizing transient absorption spectroscopy to monitor the evolution of photocycle intermediates of bR in nanodisc, the photocycle kinetics of bR was significantly retarded and the transient populations of intermediates N and O were decreased as the content of DMPG or DOPG was reduced. In this work, we not only demonstrated the usefulness of nanodiscs as a membrane mimicking system, but also showed that the surrounding lipids play a crucial role in altering the biological functions, e.g., the ion translocation kinetics of the transmembrane proteins.
II. Time-dependent quantum wave packet obtained by solving the time-dependent Schrödinger equation (TDSE) provides theoretical information for quantum phenomena of physical systems. In conventional computational methods, the finite difference method is employed to obtain approximate solutions to the TDSE. In order to improve the numerical algorithm for the TDSE, we develop the truncated grid method to reduce the computational effort by eliminating grid points with extremely low probability densities. By applying the new method to several quantum systems, including the free Guassian wave packet and the coherent state of the harmonic oscillator, the propagation behavior of wavepacket were demonstrated. In addition, we employ the truncated grid method to solve the imaginary-time Schrödinger equation for the ground and first-excited states of the harmonic oscillator, the double well potential, and the Morse potential. Excellent computational results for these examples show that the truncated grid method significantly reduces the computational effort relative to the full-grid integration for the TDSE.
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