Anticorrelated fluctuation

Figure 24.2a shows dual fluorescence intensity trajectories simultaneously recorded from a donor-acceptor labeled T4 lysozyme in the presence of substrate at pH 7.2. The anticorrelated fluctuations (Fig. 24.2a and b) are due to spFRET, reporting the donor-acceptor distance change associated with the protein conformational motion. Likewise, fluorescence trajectories of donor-acceptor labeled T4 lysozyme without substrates did not show anticorrelated behavior (Fig. 24.2c and d). We attribute this conformational motion to an enzymatic-related motion, most likely the open-closed hinge-bending motion... 

Fig. 24.2. Single-molecule recording of T4 lysozyme conformational motions and enzymatic reaction turnovers of hydrolysis of an E. coli B cell wall in real time, (a) This panel shows a pair of trajectories from a fluorescence donor tetramethyl-rhodamine blue) and acceptor Texas Red (red) pair in a single-T4 lysozyme in the presence of E. coli cells of 2.5mg/mL at pH 7.2 buffer. Anticorrelated fluctuation features are evident. (b) The correlation functions (C (t)) of donor ( A/a (0) Aid (f)), blue), acceptor ((A/a (0) A/a (t)), red), and donor-acceptor cross-correlation function ((A/d (0) A/d (t)), black), deduced from the single-molecule trajectories in (a). They are fitted with the same decay rate constant of 180 40s. A long decay component of 10 2s is also evident in each autocorrelation function. The first data point (not shown) of each correlation function contains the contribution from the measurement noise and fluctuations faster than the time resolution. The correlation functions are normalized, and the (A/a (0) A/a (t)) is presented with a shift on the y axis to enhance the view, (c) A pair of fluorescence trajectories from a donor (blue) and acceptor (red) pair in a T4 lysozyme protein without substrates present. The acceptor was photo-bleached at about 8.5 s. (d) The correlation functions (C(t)) of donor ((A/d (0) A/d (t)), blue), acceptor ((A/a (0) A/a (t)), red) derived from the trajectories in (c). The autocorrelation function only shows a spike at t = 0 and drops to zero at t > 0, which indicates that only uncorrelated measurement noise and fluctuation faster than the time resolution recorded (Adapted with permission from [12]. Copyright 2003 American Chemical Society)...

The fluorescence intensity trajectories of the donor (/d(f)) and acceptor (/a(t)) give autocorrelation times (Fig. 24.2b) indistinguishable from fitting an exponential decay to the autocorrelation functions, (A/d (0) A/d (t)) and (A/a (0) A/a (t)), where A/d(t) is /d(t) — (Id), (Id) is the mean intensity of the overall trajectory of a donor, and A/a(t) has the same definition for an intensity trajectory of an acceptor. In contrast, the cross-correlation function between the donor and acceptor trajectories, (A/d (0) A/d (t)), is anticorrelated with the same decay time (Fig. 24.2b) which supports our assignment of anticorrelated fluctuations of the fluorescence intensities of the donor and acceptor to the spFRET process. 

The anomalies of liquid water become more pronounced when it is supercooled. For example, the volume and entropy fluctuations of liquid water become more pronounced as the temperature decreases. This is in contrast to most other liquids, in which the volume and entropy fluctuations become smaller as the temperature is lowered. Furthermore, the volume and entropy fluctuations in water at less than 4°C are anticorrelated, that is, the increase in volume which occurs when water is cooled results in a decrease in entropy (Debenedetti, 2003). 

It is of interest to examine the nature of the motions of a sidechain as large as a tryptophan residue in the protein interior. Reorientation of the transition dipole vector of tryptophan is due mainly to rotation about the C —C(3 and C,3—Cr bonds, which correspond to the x1 and x2 dihedral angles of the side-chain, although larger-scale collective motions of the backbone are also involved. In the protein environment, the fluctuations of x1 and x2 are expected to be anticorrelated so that large variations in the two angles result in a... 

Figure 2. Shot noise damping in a simple model circuit demonstrates why macroscopic linear conductors are usually free from this type of noise. The circuit is a series connection of N ideal current noise generators paralleled by ideal resistors. Anticorrelations in elementary transport events arise from the voltage fluctuations in connectors between generators.

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