Advanced Collective Variables

As discussed in the previous section, one of the most difficult issues in running metadynamics simulations is that of choosing a proper set of CVs. The limited reliability of metadynamics calculations is often mistakenly perceived as a limitation of the method although the real reason is generally due to the descriptors used. 

A good CV that is able to distinguish reactants and products may not be sufficient in driving the reaction reversibly. This is due to the fact that a 

We also discussed how important it is to devise a CV that can also produce a force in a direction that permits the system to travel between all relevant configurations. 

For these reasons it is typically more useful to explore multiple sets of CVs rather than to tune the other metadynamics parameters. Moreover, moving toward a better sampling by attempting various CV sets always implies a better understanding of the physicochemical process being studied. 

Given the inherent difficulty of making such a choice, much effort in the past decade has been focused on developing CVs suitable to describe correctly a variety of conformational changes. We review here a few of the most popular choices used with metadynamics but which can also be used in other schemes like umbrella sampling, thermodynamic integration, and steered molecular dynamics. 

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In Section Advanced Collective Variables we will discuss ad hoc solutions for finding CVs that are optimal for specific problems. For the time being, we refer to the example of alanine dipeptide and try to identify the relevant... 

With rapid advances in hardware, database management and information processing systems, efficient and competitive manufacturing has become an information-intensive activity. The amounts of data presently collected in the field on a routine basis are staggering, and it is not unusual to find plants where as many as 20,000 variables are continuously monitored and stored (Taylor, 1989). 

The restrictor controls the flow rate of the SFE system. It is positioned after the extraction cell and ends in a collection device (off-line SFE) or in the injection port of another analytical device (on-line SFE). A shutoff valve is typically placed between the restrictor and extraction cell to enable static extractions to occur. A review of the literature indicates that the restrictor is one of the more problematic aspects of SFE. Restrictors are prone to plugging by ice formation, caused by expansion cooling of the supercritical fluid at the outlet of the restrictor, or by extracted material from the sample matrix. The technology of restrictors as flow-control devices in SFE has made significant advances since initial descriptions30 and has redefined restrictors as either fixed flow or variable flow. 

GFR in this patient population. Huang and associates reported the inability of several CLc, equations to predictrenal function in hospitalized patients with advanced human immunodeficiency virus disease. All methods, including CG, Jelliffe, and Mawer, overestimated the measured 24-hour CLc,. The reasons for the poor predictability of these methods is unclear, although 24-hour collection methods often yield highly variable results because of inadequate urine collection. 

In complete analogy to NMR, FT EPR has been extended into two dimensions. Two-dimensional correlation spectroscopy (COSY) is essentially subject to the same restrictions regarding excitation bandwidth and detection deadtime as was described for one-dimensional FT EPR. In 2D-COSY EPR a second time dimension is added to the FID collection time by a preparatory pulse in front of the FID detection pulse and by variation of the evolution time between them (see figure B1.15.10(B)). The FID is recorded during the detection period of duration t, which begins with the second 7r/2-pulse. For each the FID is collected, then the phase of the first pulse is advanced by 90°, and a second set of FIDs is collected. The two sets of FIDs, whose amplitudes oscillate as functions of t, then undergo a two-dimensional complex Fourier transformation, generating a spectrum over the two frequency variables co and co,. 

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