Functional Motions

The use of such renormalized or coarser-grained models of biomolecules fend to have the most success on very large structures (over 3000 residues). Recognition that exact atomic coordinates are unnecessary, has allowed the application of EN models to assist in the refinement of low-resolution experimental data from cryo-EM [18] and X-ray [22,23]. This refinement application involves perturbing a known or approximate structure along a set of low-frequency modes until it better matches the experimental data [24]. 

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Normal mode analysis exists as one of the two main simulation techniques used to probe the large-scale internal dynamics of biological molecules. It has a direct connection to the experimental techniques of infrared and Raman spectroscopy, and the process of comparing these experimental results with the results of normal mode analysis continues. However, these experimental techniques are not yet able to access directly the lowest frequency modes of motion that are thought to relate to the functional motions in proteins or other large biological molecules. It is these modes, with frequencies of the order of 1 cm , that mainly concern this chapter. 

Equation (8) shows that it is the fluctuations of the lowest frequency modes that contribute most to the overall fluctuation of the molecule. For example, in the case of lysozyme, the lowest frequency nonnal mode (out of a total of 6057) accounts for 13% of the total mass-weighted MSF. It is for this reason that it is common to analyze just the lowest frequency modes for the large-scale functional motions. 

One of the main attractions of normal mode analysis is that the results are easily visualized. One can sort the modes in tenns of their contributions to the total MSF and concentrate on only those with the largest contributions. Each individual mode can be visualized as a collective motion that is certainly easier to interpret than the welter of information generated by a molecular dynamics trajectory. Figure 4 shows the first two normal modes of human lysozyme analyzed for their dynamic domains and hinge axes, showing how clean the results can sometimes be. However, recent analytical tools for molecular dynamics trajectories, such as the principal component analysis or essential dynamics method [25,62-64], promise also to provide equally clean, and perhaps more realistic, visualizations. That said, molecular dynamics is also limited in that many of the functional motions in biological molecules occur in time scales well beyond what is currently possible to simulate. 

Evidence exists that some of the softest normal modes can be associated with experimentally determined functional motions, and most studies apply normal mode analysis to this purpose. Owing to the veracity of the concept of the normal mode important subspace, normal mode analysis can be used in structural refinement methods to gain dynamic information that is beyond the capability of conventional refinement techniques. 

The correlation functions for the Lotka model in the auto-oscillating regime are presented in Figs 8.14 and 8.15. The value of the parameter k = 0.02 corresponds to the curves plotted in Figs 8.7(c) and 8.8. The correlation functions motion is completely periodic, the results shown here correspond to the the minimum and maximum of K(t). 

The scheme proposed by Car and Parinello1 in 1985 offers an attractive solution to this problem, by propagating the wave-function together with the nuclei. The ingenious idea of Car and Parinello was to include the fictitious kinetic energy term describing the wave-function motion into the classical Lagrangian ... 

The reason why the condition of Eq. (275) yields the breakdown of the correspondence between quantum and classical mechanics is evident. The quantum wave function can be identified with a trajectory if it is sharp enough, namely if U(t) < 2(f). When the width of the wave function becomes as large as the width of the channel, within which the wave function moves, the wave function motion starts to depend on the structure of the surrounding phase space, and the correspondence is broken. Using a geometrical model making E(t) decrease exponentially with time [122], the condition of Eq. (275) is shown to occur at time t = tB, where... 

In order to understand how proton NMR of polymers may be used as presented in the current chapter, it is useful to remind ourselves of some of the results of the formalism used in describing the time-dependent quantum mechanics of spin which are not so well understood by those familiar with only the rudimentary pulse NMR experiment. We do so in Section 6.1.2. In Section 6.1.3, examples are given of the uses of the mechanics outlined in Section 6.1.2 to provide information about chemical functionality, motion... 

Fishing for Functional Motions with Elastic Network Models... 

Yang, L.W., et al. iGNM a database of protein functional motions based on Gaussian network model. Bioinformatics 2005,21, 2978. 

Doruker, R, Jernigan, R.L. Functional motions can be extracted from on-lattice construction of protein structures. Proteins 2003, 53,174. 

Li, G. H. and Cui, Q. (2004) Analysis of functional motions in Brownian molecular machines with an efficient block normal mode approach Myosin-II and Ca +-ATPase, Biophys. J. 86, 743-763. 

This brief survey conveys the broad range of timescales and variety of functional motions that have been revealed through studies of VER process in heme proteins. 

Modeling of a human body with the emphasis to the extremities is the prerequisite for the synthesis of analytic control [3(U33]. Human extremities are unlike any other plant encountered in control engineering especially in terms of joints, actuators, and sensors. This fact must be kept in mind when applying the general equations of mechanics to model the dynamics of functional motions. A simple extension of analytical tools used for the modeling of mechanical plants to the modeling of biomechanical s) tems may easily produce results in sharp discrepancy to reality. 

In full extension the femur rolls, slides, and spins. The motion is multiplanar and involves more than one axis it is said to occur on a helical axis. The hehcal axis conqiletely defines a three-dimensional motion between two rigid bodies. Active functional motions, appendicular as well as vertebral, are usually motions about helical axes. 

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