Moving boundary truncated grid method for electronic nonadiabatic dynamics.

The moving boundary truncated grid method is developed to study the wave packet dynamics of electronic nonadiabatic transitions between a pair of diabatic potential energy surfaces. The coupled time-dependent Schrödinger equations (TDSEs) in the diabatic representation are integrated using adaptive truncated grids for both the surfaces. As time evolves, a variable number of grid points fixed in space are activated and deactivated without any advance information of the wave packet dynamics. Essential features of the truncated grid method are first illustrated through applications to three one-dimensional model problems, including the systems of single avoided crossing, dual avoided crossing, and extended coupling region with reflection. As a demonstration for chemical applications, the truncated grid method is then employed to study the dynamics of photoisomerization of retinal in rhodopsin described by a two-electronic-state two-dimensional model. To demonstrate the capability of the truncated grid method to deal with the electronic nonadiabatic problem in high dimensionality, we consider a multidimensional electronic nonadiabatic system in two, three, and four dimensions. The results indicate that the correct grid points are automatically activated to capture the growth and decay of the wave packets on both of the surfaces. Therefore, the truncated grid method greatly decreases the computational effort to integrate the coupled TDSEs for multidimensional electronic nonadiabatic systems.

Moving Boundary Truncated Grid Method: Application to the Time Evolution of Distribution Functions in Phase Space.

The moving boundary truncated grid (TG) method, previously developed to integrate the time-dependent Schrödinger equation and the imaginary time Schrödinger equation, is extended to the time evolution of distribution functions in phase space. A variable number of phase space grid points in the Eulerian representation are used to integrate the equation of motion for the distribution function, and the boundaries of the TG are adaptively determined as the distribution function evolves in time. Appropriate grid points are activated and deactivated for propagation of the distribution function, and no advance information concerning the dynamics in phase space is required. The TG method is used to integrate the equations of motion for phase space distribution functions, including the Klein-Kramers, Wigner-Moyal, and modified Caldeira-Leggett equations. Even though the initial distribution function is nonnegative, the solutions to the Wigner-Moyal and modified Caldeira-Leggett equations may develop negative basins in phase space originating from interference effects. Trajectory-based methods for propagation of the distribution function do not permit the formation of negative regions. However, the TG method can correctly capture the negative basins. Comparisons between the computational results obtained from the full grid and TG calculations demonstrate that the TG method not only significantly reduces the computational effort but also permits accurate propagation of various distribution functions in phase space.

Highly Efficient Transfer of 7TM Membrane Protein from Native Membrane to Covalently Circularized Nanodisc.

Incorporating membrane proteins into membrane mimicking systems is an essential process for biophysical studies and structure determination. Monodisperse lipid nanodiscs have been found to be a suitable tool, as they provide a near-native lipid bilayer environment. Recently, a covalently circularized nanodisc (cND) assembled with a membrane scaffold protein (MSP) in circular form, instead of conventional linear form, has emerged. Covalently circularized nanodiscs have been shown to have improved stability, however the optimal strategies for the incorporation of membrane proteins, as well as the physicochemical properties of the membrane protein embedded in the cND, have not been studied. Bacteriorhodopsin (bR) is a seven-transmembrane helix (7TM) membrane protein, and it forms a two dimensional crystal consisting of trimeric bR on the purple membrane of halophilic archea. Here it is reported that the bR trimer in its active form can be directly incorporated into a cND from its native purple membrane. Furthermore, the assembly conditions of the native purple membrane nanodisc (PMND) were optimized to achieve homogeneity and high yield using a high sodium chloride concentration. Additionally, the native PMND was demonstrated to have the ability to assemble over a range of different pHs, suggesting flexibility in the preparation conditions. The native PMND was then found to not only preserve the trimeric structure of bR and most of the native lipids in the PM, but also maintained the photocycle function of bR. This suggests a promising potential for assembling a cND with a 7TM membrane protein, extracted directly from its native membrane environment, while preserving the protein conformation and lipid composition.

Moving Boundary Truncated Grid Method for Wave Packet Dynamics.

The moving boundary truncated grid method is developed to significantly reduce the number of grid points required for wave packet propagation. The time-dependent Schrödinger equation (TDSE) and the imaginary time Schrödinger equation (ITSE) are integrated using an adaptive algorithm which economizes the number of grid points. This method employs a variable number of grid points in the Eulerian frame (grid points fixed in space) and adaptively defines the boundaries of the truncated grid. The truncated grid method is first applied to the time integration of the TDSE for the photodissociation dynamics of NOCl and a three-dimensional quantum barrier scattering problem. The time-dependent truncated grid precisely captures the wave packet evolution for the photodissociation of NOCl and finely adjusts according to the process of the wave packet bifurcation into reflected and transmitted components for the barrier scattering problem. The truncated grid method is also applied to the time integration of the ITSE for the eigenstates of quantum systems. Compared to the full grid calculations, the truncated grid method requires fewer grid points to achieve high accuracy for the stationary state energies and wave functions for a two-dimensional double well potential and the Ar trimer. Therefore, the truncated grid method demonstrates a significant reduction in the number of grid points needed to perform accurate wave packet propagation governed by the TDSE or the ITSE.

Tuning the Photocycle Kinetics of Bacteriorhodopsin in Lipid Nanodiscs.

Monodisperse lipid nanodiscs are particularly suitable for characterizing membrane protein in near-native environment. To study the lipid-composition dependence of photocycle kinetics of bacteriorhodopsin (bR), transient absorption spectroscopy was utilized to monitor the evolution of the photocycle intermediates of bR reconstituted in nanodiscs composed of different ratios of the zwitterionic lipid (DMPC, dimyristoyl phosphatidylcholine; DOPC, dioleoyl phosphatidylcholine) to the negatively charged lipid (DOPG, dioleoyl phosphatidylglycerol; DMPG, dimyristoyl phosphatidylglycerol). The characterization of ion-exchange chromatography showed that the negative surface charge of nanodiscs increased as the content of DOPG or DMPG was increased. The steady-state absorption contours of the light-adapted monomeric bR in nanodiscs composed of different lipid ratios exhibited highly similar absorption features of the retinal moiety at 560 nm, referring to the conservation of the tertiary structure of bR in nanodiscs of different lipid compositions. In addition, transient absorption contours showed that 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. This observation could be attributed to the negatively charged lipid heads of DMPG and DOPG, exhibiting similar proton relay capability as the native phosphatidylglycerol (PG) analog lipids in the purple membrane. 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.