We have recently proposed a new unified theoretical scheme (the “middle” scheme) for thermostat algorithms for efficient and accurate configurational sampling of the canonical ensemble. In this paper, we extend the “middle” scheme to molecular dynamics algorithms for configurational sampling in systems subject to constraints. Holonomic constraints and isokinetic constraints are used for demonstration. Numerical examples indicate that the “middle” scheme presents a promising approach to calculate configuration-dependent thermodynamic properties and their thermal fluctuations.

We show a unified second-order scheme for constructing simple, robust and accurate algorithms for typical thermostats for configurational sampling for the canonical ensemble. When Langevin dynamics is used, the scheme leads to the BAOAB algorithm that has been recently investigated.We show that the scheme is also useful for other types of thermostat, such as the Andersen thermostat and Nosé-Hoover chain, regardless of whether the thermostat is deterministic or stochastic. In addition to analytical analysis, two 1-dimensional models and three typical realistic molecular systems that range from the gas phase, clusters, to the condensed phase are used in numerical examples for demonstration. Accuracy may be increased by an order of magnitude for estimating coordinate-dependent properties in molecular dynamics (when the same time interval is used), irrespective of which type of thermostat is applied. The scheme is especially useful for path integral molecular dynamics, because it consistently improves the efficiency for evaluating all thermodynamic properties for any type of thermostat.4

This study constructs a rat brain T2-weighted magnetic resonance imaging template including olfactory bulb and a compatible digital atlas. The atlas contains 624 carefully delineated brain structures based on the newest (2005) edition of rat brain atlas by Paxinos and Watson. An automated procedure, as an SPM toolbox, was introduced for spatially normalizing individual rat brains, conducting statistical analysis and visually localizing the results in the Atlas coordinate space. The brain template/atlas and the procedure were evaluated using functional images between rats with the right side middle cerebral artery occlusion (MCAO) and normal controls. The result shows that the brain region with significant signal decline in the MCAO rats was consistent with the occlusion position.