Dynamics of Macromolecules

For a given potential energy function, one may take a variety of approaches to study the dynamics of macromolecules. The most exact and detailed information is provided by MD simulations in which one solves the equations of motion for the atoms constituting the macromolecule and any surrounding environment. With currently available techniques and methods it is possible... 

J. Kleia, Molecular Conformation and Dynamics of Macromolecules in Condensed Systems, Elsevier, Amsterdam, 1988, p. 333. 

FRET in many different environments following dynamics of macromolecules... 

Chance, M.R. Sclavi, B. Woodson, S.A. Brenowitz, M. Examining the conformational dynamics of macromolecules with time-resolved synchrotron X-ray footprintmg . Structure 1997, 5, 865—869. 

Tanaka T (1988) In Nagasawa M (ed) Molecular conformation and dynamics of macromolecules in condensed systems. Elsevier, New York... 

The most advanced theories of relaxation phenomena in a system of entangled macromolecules is based on the dynamics of a single macromolecule. Dynamics of the tagged macromolecule is simplified by the assumption that the neighbouring macromolecules can be described as a uniform structureless medium and all important interactions can be reduced to intramolecular interactions. The dynamic equation for a macromolecule can be written as a modification of equation (2.1) for dynamics of macromolecule in viscous liquid... 

Particular cases of dynamic equation (3.11) were investigated by Ronca (1983) and by Hess (1986, 1988) who apparently did not know about previously published results. They made unsuccessful attempts to describe dynamics of macromolecule in an entangled system without the second dissipative term which is connected with the internal resistance forces. One can see in subsequent chapters that the properties of polymer melts cannot be understood correctly without this term. The importance of the internal resistance term was recognised by Pokrovskii and Volkov (1978b) after the first attempt to tackle the problem (Pokrovskii and Volkov 1978a). 

It is instructive to compare the system of equations (3.46) and (3.47) with the system (3.37). One can see that both the radius of the tube and the positions of the particles in the Doi-Edwards model are, in fact, mean quantities from the point of view of a model of underlying stochastic motion described by equations (3.37). The intermediate length emerges at analysis of system (3.37) and can be expressed through the other parameters of the theory (see details in Chapter 5). The mean value of position of the particles can be also calculated to get a complete justification of the above model. The direct introduction of the mean quantities to describe dynamics of macromolecule led to an oversimplified, mechanistic model, which, nevertheless, allows one to make correct estimates of conformational relaxation times and coefficient of diffusion of a macromolecule in strongly entangled systems (see Sections 4.2.2 and 5.1.2). However, attempts to use this model to formulate the theory of viscoelasticity of entangled systems encounted some difficulties (for details, see Section 6.4, especially the footnote on p. 133) and were unsuccessful. 

Notwithstanding the simplifying assumptions in the dynamics of macromolecules, the sets of constitutive relations derived in Section 9.2.1 for polymer systems, are rather cumbersome. Now, it is expedient to employ additional assumptions to obtain reasonable approximations to many-mode constitutive relations. It can be seen that the constitutive equations are valid for the small mode numbers a, in fact, the first few modes determines main contribution to viscoelasticity. The very form of dependence of the dynamical modulus in Fig. 17 in Chapter 6 suggests to try to use the first modes to describe low-frequency viscoelastic behaviour. So, one can reduce the number of modes to minimum, while two cases have to be considered separately. 

Mitsuru Nagasawa, Studies in Polymer Science 2 Molecular Conformation and Dynamics of Macromolecules in Condensed Systems. Based on lectures presented at the 1st Toyota Conference, Inuyama City, Japan, 28 September-1 October 1987, Elsevier, Amsterdam, The Netherlands, 1988. 

Albani, J.R. (2004). Structure and Dynamics of Macromolecules Absorption and Fluorescence Studies, Elsevier, Amsterdam. 

Macromolecules display continuous motions. These motions can be of two main types the molecule can rotate on itself, following the precise axis of rotation, and it can have a local flexibility. Local flexibility, also called internal motions, allows different small molecules, such as solvent molecules, to diffuse along the macromolecule. This diffusion is generally dependent on the importance of the local internal dynamics. Also, the fact that solvent molecules can reach the interior hydrophobic core of macromolecules such as proteins clearly means that the term hydrophobicity should be considered as relative and not as absolute. Internal dynamics of proteins allow and facilitate a permanent contact between protein core and the solvent. Also, this internal motion permits small molecules such as oxygen to diffuse within the protein core. Since oxygen is a collisional quencher, analyzing the fluorescence data in the presence of different oxygen concentrations yields information on the internal dynamics of macromolecules. 

It is noteworthy that strict topological constraints do not exist for systems of linear chains with free ends and do not affect the statistical properties of linear polymers nevertheless, they significantly influence the dynamics of macromolecules. 

Both the structures and the dynamics of macromolecules are studied in terms of statistical thermodynamics. In the following section, we introduce the helix-coil transition theory that accounts for formation of the ubiquitous a-helical structure of peptide chains in aqueous solution. To a large extent, current research on protein... 

In the second part, we collect contributions concerning dynamical processes in complex systems such as clusters and proteins. Here, we also include those ideas related to data mining, since this topic is an indispensable part of the studies on dynamics of macromolecules. 

The object of NMR spectroscopy on proteins, nucleic acids and other complex polymers is to obtain information on their structure and dynamics. Assignment of individual spectral lines discussed in the preceding section is a prerequisite to one s ability to decipher this information. Actually to do so it is also necessary to understand the nature of the structural and dynamic information inherent in each feature of the spectrum. And one is rightfully asked is the nature of this information such that the result will be worth the labor required to obtain a significant set of assignments An important part of the answer to this question is that NMR is the ONLY physical method which can provide any information at essentially atomic resolution on the structure and dynamics of macromolecules in solution, as well as in the solid state. Whatever the limits of this information, it is better than none. Knowledge of these limits, as well as of the nature of spectroscopic information, is nevertheless necessary, both to realize expectations and to avoid conclusions that go beyond the capabilities of the method. The information content and its limits can be meaningfully discussed for each measured parameter separately, and the common features summarized at the end. 

To obtain the accuracy required for a realistic analysis of the structure and dynamics of macromolecules it is necessary to use a relatively complex form for the empirical potential function and to optimize the values of the parameters that determine the magnitudes of the different contributing terms. In general, the function will have terms that depend not only on the relative position of all pairs of atoms but certain triples and quadruples of atoms as well. Usually, one does not need to go beyond four-body terms in the model potential function. This approach to calculating energies is often referred to as molecular mechanics.6061... 

M. Levitt, Chem. Scripta, 29A, 197 (1989). Molecular Dynamics of Macromolecules in Water. 

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