Measuring distances

The measurement of surface forces calls for a rigid apparatus that exhibits a high force sensitivity as well as distance measurement and control on a subnanometre scale [38]. Most SFAs make use of an optical interference teclmique to measure distances and hence forces between surfaces. Alternative distance measurements have been developed in recent years—predominantly capacitive techniques, which allow for faster and simpler acquisition of an averaged distance [H, 39, 40] or even allow for simultaneous dielectric loss measurements at a confined interface. 

Frantz P, Agrait N and Salmeron M 1996 Use of capacitance to measure surface forces. 1. Measuring distance of separation with enhanced spacial and time resolution Langmuir 12 3289-94... 

Internal dynamics of the macromolecule influences all experimental data that can be measured by NMR. The weighting of the NOE makes the averaging very nonlinear, and the measured distance may appear much shorter than the average distance (see Eig. 9). 

Figure 9 Treating internal dynamics during the refinement process. Due to dynamics and the weighting of the NOE, the measured distance may appear much shorter than the average distance. This can be accounted for by using ensemble refinement techniques. In contrast to standard refinement, an average distance is calculated over an ensemble of C structures (ensemble refinement) or a trajectory (time-averaged refinement). The time-averaged distance is defined with an exponential window over the trajectory. T is the total length over the trajectory, t is the time, and x is a relaxation time characterizing the width of the exponential window.

Some general quantitative characteristics (orders of magnitudes) of LDA systems are velocity measurement range 1 mm s -100 m s relative measurement uncertainty 0.1-1% rate of accepted data 0.1-10 kHz size of the optical probe 10 p.m-1 mm for each dimension measuring distance 0.1-1 m. 

As the measuring distance for such equipment can be up to about. 50 m, this technique is advantageous in cases when conventional acoustic or vibro-meter devices are difficult or even impossible to use, such as high-frequency vibration measurements on the walls of high-level air ducts. 

Experimental distances from NOEs/ROEs of small molecules are recommended not to be classified into regions of small, medium, and large as it is often done in the structure determination of large molecules. As opposed to macromolecules, the overall correlation time Tc can be considered constant in small molecules. Thus, it is possible to measure distances in the range between 2 and 5 A with an accuracy of about 10%. Often distances between protons are almost exclusively used for the structure determination. This leads to the fact that molecules with small numbers of hydrogen atoms are more difficult to determine. 

Minimizing this function is equivalent to finding a low-dimensional configuration of points which has Euclidean object-to-object distances by as close as possible to some transformation/(.) of the original distances or dissimilarities, dy. Thus, the model distances by are not necessarily fitted to the original dy, as in classical MDS, but to some admissible transformation of the measured distances. For example, when the transformation is a general monotonic transformation it preserves the... 

Polyvinyl chloride cylinders -1- nylon gauze -1- device for continuous water supply Soil slices at measurable distance from soil-root interface. High bulk density of soil sampled. Nutrient uptake through an induced root hairs surface. Study of rhizosphere effect over a time and distance gradient from the soil-root interface. 47, 67, 127-129... 

Measured distance (inches) in a tube of constant diameter. 

EPR studies of host-guest complexes of carotenoids Measuring distances between carotenoid radicals and distant metals in matrices by using ESEEM methods and pulsed EPR relaxation techniques EPR studies of radical cations on activated alumina and silica-alumina... 

To measure distances in the wider temperature range, this procedure was modified. Relaxation of the carotenoid occurs through several different mechanisms including the dipolar-dipolar interaction. Assuming that kAA is the rate constant of the dipolar-dipolar interaction and K=(k,l + k2 + k3 +. ..) is the sum of the rate constants of all other relaxation pathways, we can extract kAA from the following equation ... 

A satisfactory fuse must be capable of propagating laterally from one line to another. In this way it is practicable to join lengths of fuse by ordinary knots, such as the reef knot. In test, the usual method is-to lay two strands of fuse at a measured distance apart and ascertain that one... 

Although the stabilizing interactions between the amino acid side chains of PLC/j, and the choline headgroup are readily apparent in the PLC fc-phosphonate inhibitor complex, it is more difficult to identify contacts between the protein and the acyl chains of the inhibitor [45]. In part this is because thermal motion in the acyl side chains, especially the sn-1 chain, renders them somewhat disordered. Consequently, the measured distances between the side chain carbons... 

The superposition principle allows us to assume just a single scatterer in the view of the radar. The transmitted signal hits this scatterer whose distance (we measure distance and time in the same units) from the (collocated) transmitter and receiver is r. Assume that the scatterer is stationary. The return signal will be a delayed version of the original, delayed by the total round trip time from the radar to the scatterer. Specifically the signal voltage at the antenna of the receiver is... 

The right panel of Figure 1.3 displays the radial function obtained by Fourier transformation of the -weighed background-subtracted EXAFS data from the solid heated to 420°C [31], This spectrum shows two major peaks, one at about 1.5 A associated with backscattering from O neighbors, and a second at 3 A related to the Nb-Mo pairs. The measured distances are consistent with a combination of niobium oxo species and heteropolymolybdate fragments, presumably the catalytically active phase. 

The use of Forster non-radiative energy transfer for measuring distances at a supramolecular level (spectroscopic ruler) will be discussed in detail in Chapter 9. 

TIRF can be combined with fluorescence energy transfer to measure distances between fluorophores on a surface in the presence of a large background of bulk-dissolved fluorophores. 

Fluorescence resonance energy transfer (FRET) is a technique that has been used to measure distances between pairs of proximal fluorochromes. A suitable pair consists of a donor fluorochrome, which has an emission spectrum... 

S)-warfarin were used as the templates. This substrate superposition was supported by an NMR study measuring distances between the heme-iron and the substrate protons (66). The model featured (1) anionic heteroatom (A-) at a distance of approx 4 A from a hypothetical cationic site (C+) of the protein,... 

Figure 6.4 shows a schematic view of a one-dimensional energy profile that has the same shape as the result in Fig. 6.3. Figure 6.4 is drawn in terms of a reaction coordinate, x, that measures distance along the path connecting the two local minima at x A and x B. The saddle point located at x that separates the two minima is called the transition state. We will refer to all points in Fig. 6.4 to the left (right) of the transition state as state A (state B). 

---