Dynamics of macromolecular interactions

Theoretical approaches to structural biophysics, like the theories of transport and reaction kinetics explored in other chapters of this book, are grounded in physical chemistry concepts. Here we explore a few problems in molecular structural dynamics using those concepts. The first two systems presented, helix-coil transitions and actin polymerization, introduce classic theories. The material in the remainder of the chapter arises from the study of macromolecular interactions and is motivated by current research aimed at uncovering and understanding how large numbers of proteins (hundreds to thousands) interact in cells [7],... 

With the increased level of understanding of the cyclization dynamics as monitored by intramolecular excimer fluorescence, it is now possible to extend this probe to the study of systems more complex than dilute solutions. One such situation involves the structure and dynamics of macromolecular complexes formed between polymeric proton donors and acceptors in aqueous solution. For example, there has been widespread interest in the complexes formed between poly(ethylene glycol) and poly(acrylic acid) or poly(methacrylic acid) in aqueous solution (34, 35). A second, complicated morphological problem is to describe the configurational behavior of polymer chains adsorbed on colloidal particles. This research has relevance to the understanding of steric stabilization. One system of particular interest is the interaction of poly(ethylene glycol) and colloidal silica (36-40). 

Piszczek, G., Luminescent metal-ligand complexes as probes of macromolecular interactions and biopolymer dynamics. Archives Biochem. Biophys. 2006,453, 54—62. 

CONTENTS Preface. C. Allen Bush. Methods in Macromolecular Crystallography, Andrew J. Howard and Thomas L. Poulos. Circular Dichroism and Conformation of (Jnordered Polypeptides. Robert W. Woody. Luminescence Studies with Horse Liver Dehydrogenase Information on the Structure, Dynamics. Transitions and Interactions of this Enzyme. Maurice R. Eftink. Surface-Enhanced Resonance Raman Scattering (SERFS) Spectroscopy A Probe of Biomolecular Structure and Bonding at Surfaces. Therese M. Cotton, Jae-Ho Kim and Randall E. Holt. Three-Dimensional Conformations of Complex Carbohydrates. C. Allen Bush and Porseveranda Cages. Index. 

The set of stochastic equations given by (3.37) is equivalent (in the linear case) to equations (3.11) with the memory functions defined in Section 3.3, but, in contrast to equations (3.11), set (3.37) is written as a set of Markov stochastic equations. This enables us to determine the variables that describe the collective motion of the set of macromolecules. In this particular approximation, the interaction between neighbouring macromolecules ensures that the phase variables of the elementary motion are co-ordinates, velocities, and some other vector variables - the extra forces. This set of phase variables describes the dynamics of the entire set of entangled macromolecules. Note that the Markovian representation of the equation of macromolecular dynamics cannot be made for any arbitrary case, but only for some simple approximations of the memory functions. We are considering the case with a single relaxation time, but generalisation for a case with a few relaxation times is possible. 

The dynamic modulus of the suspension of non-interacting macromolecular coils is determined by three sets of relaxation times... 

The solution behavior of polymers has been intensively investigated in the past. Dilute solutions, where polymer-polymer interactions may be excluded, have become the basis for the characterization of the primary structure of macromolecules and their dimensions in solution. Besides this "classical" aspect of macromolecular science, interest has focussed on systems, where - due to strong polymer/polymer interactions - association of polymers causes supermolecular structures in homogeneous thermo-dynamically-stable isotropic and anisotropic solutions or in phase-separated multi-component systems. The association of polymers in solutions gives rise to unconventional properties, yielding new aspects for applications and multiple theoretical aspects. 

Although the structure of the macromolecule alone is of less interest than that of the complex, in many cases a determination of the structure of the complex follows from earlier studies on the unbound macromolecule. It is thus useful to describe the approaches to structure determination of macromolecular targets. This is followed by a discussion of the dynamic aspects of protein structures in Section 3.2, before addressing the main topic of macromolecule-ligand interactions in Section 3.3. 

---