Macromolecules in solution

In dilute solution, the behavior of macromolecules is quite different to that of common low-molecular-weight molecules. For example, the shape of a macro-molecular coil is subject to permanent dynamic changes, and the coils are in a more or less swollen state when compared to their unperturbed (solid state) 

End-to-end distances are parameters that are easy to calculate by theoretical approaches but cannot be measured directly. On the other hand, the radius of gyration is a quantity readily accessible by experiment. For M —4 general relationships exist between the radius of gyration and the end-to-end distance for all linear chains with only short-range interactions, for example r = 6 s . 

1 Consider the concept that primary structure leads to a functional protein as described by Anfinsen s experiments with ribonuclease. Why was it fortunate that Anfinsen worked with ribonuclease Would the same conclusions been found if the protein insulin had been used. 

2 What is the AGr from ethanol to water of a peptide comprised of three serines compared to one with three glycines Instead of serines, calculate it for three phenyalanines Which peptide is more hydrophobic and why  

5 What are two limiting-case models for protein folding How do they differ  

6 Wliat is the primary component of the amyloid plaques associated with Alzheimer s disease  

This chapter from The Physical Basis of Biochemistry Solutions Manual to the Second Edition corresponds to Chapter 18 from The Physical Basis of It iochemist ly, Second Edition 

Polymer solutions are important because many polymer syntheses as well as most procedures for their molecular characterization are carried out in solution. Polymer solutions are furthermore essential in the processing of some polymers to fibers, preparation of polymer blends, coatings, and adhesives. Moreover, polymer solutions are applied because of their high viscosity (thickeners). Last but not least. 

The simplest theoretical chain model of a macromolecule assumes the polymer to be a linear chain composed of M -i- 1 chain atoms, connected by N bonds of identical length b. The mathematically maximum possible chain length is L = Nb. 

Many techniques of polymer characterization are performed when the polymer molecules are in solution. This is because the thermodynamic properties of polymer solutions can be readily measured and the results interpreted in terms of the size and structure of the macromolecules and so enabling characterization of the polymer. Because of the importance of polymer solutions it is necessary, first of all, to consider the conformations that polymer molecules adopt in solutions and then go on to look at the various theories which have been developed to explain the thermodynamic properties of polymer solutions. 

Although these considerations are only for n-butane it is possible to extend them with certain reservations to longer molecules such as polyethylene. In general, each successive linkage will have three possible 

There are also other conformations where there is interference between segments of the molecule and so in general not all combinations of trans and gauche positions are possible along a given chain. 

An equivalent measure of the dimensions of a simple chain is the RMS radius of gyration s Y which is the RMS distance of the elements of the cham from its centre of gravity. It can be shown that s Y is related simply to r Y through the equation 

It must be stressed that this function, which is plotted in Fig. 3.7(a) is the probability per volume of the chain end being at x,y,z) and has a maximum at the origin. We are normally interested in the probability of the chain end being at a distance r in any direction from the origin. This can be readily determined by calculating the probability of finding the chain end in a spherical shell of thickness dr and radius r and centred at the origin. The volume dV of such a shell is then 

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Watanabe, M., Karplus, M. Dynamics of Molecules with Internal Degrees of Freedom by Multiple Time-Step Methods. J. Chem. Phys. 99 (1995) 8063-8074 Figueirido, F., Levy, R. M., Zhou, R., Berne, B. J. Large Scale Simulation of Macromolecules in Solution Combining the Periodic Fast Multiple Method with Multiple Time Step Integrators. J. Chem. Phys. 106 (1997) 9835-9849 Derreumaux, P., Zhang, G., Schlick, T, Brooks, B.R. A Truncated Newton Minimizer Adapted for CHARMM and Biomolecular Applications. J. Comp. Chem. 15 (1994) 532-555... 

Morawitz, H., Macromolecules in Solution, Interscience, New York, 1965. Richards, E. G., An Introduction to the Physical Properties of Large Molecules in Solution, Cambridge University Press, Cambridge, 1980. 

The advantage of the LB technique is that it allows systematic studies of 2-D organization, both before and after transfer from the air—water interface onto a soHd substrate. However, the coupling of 3-D self-organization of macromolecules in solution with organization at a soHd surface may best be achieved using the self-assembly technique. 

A very simple version of this approach was used in early applications. An alchemical charging calculation was done using a distance-based cutoff for electrostatic interactions, either with a finite or a periodic model. Then a cut-off correction equal to the Born free energy, Eq. (38), was added, with the spherical radius taken to be = R. This is a convenient but ill-defined approximation, because the system with a cutoff is not equivalent to a spherical charge of radius R. A more rigorous cutoff correction was derived recently that is applicable to sufficiently homogeneous systems [54] but appears to be impractical for macromolecules in solution. 

G. D. J. Phillies. Universal scaling equation for self-diffusion by macromolecules in solution. Macromolecules 79 2367-2376, 1986 Dynamics of polymers... 

MorawetzH (1965) Macromolecules in Solutions. Interscience — J Wiley, New York, p 92... 

There are a few instances where a macromolecule in solution can be degraded even in the absence of an elongational flow field. In these circumstances, the chain scission was believed to happen in a partly extended state this situation is sufficiently related to the degradation in transient elongational flow to be worth... 

Muller AJ (1989) Extensional flow of macromolecules in solution, Ph D Thesis, University of Bristol, Physics Department... 

Tsvetkov VN, Eskin V, Frenkel S (1970) Structure of Macromolecules in Solution. Butterworths, London... 

It is very difficult and scarce to find literature to study the electrokinetic phenomena of proteins or macromolecules in solution therefore limit us to the basic concepts of electrokinetic changes observed, they are conformational change because of the presence of salts and the zeta potential change in pH. 

Multiple Linear Least-Squares Fits with a Common Intercept Determination of the Intrinsic Viscosity of Macromolecules in Solution. Journal of Chemical Education 80(9), 1036-1038. 

A field of application of MD that is beginning to bear fruit is the refinement of data from nuclear magnetic resonance (NMR) and from diffraction experiments. High-resolution NMR at frequencies around 500 MHz is able to resolve individual proton resonances of biological macromolecules in solution with molecular weights exceeding 10,000... 

Diffusion of flexible macromolecules in solutions and gel media has also been studied extensively [35,97]. The Zimm model for diffusion of flexible chains in polymer melts predicts that the diffusion coefficient of a flexible polymer in solution depends on polymer length to the 1/2 power, D N. This theoretical result has also been confirmed by experimental data [97,122]. The reptation theory for diffusion of flexible polymers in highly restricted environments predicts a dependence D [97,122,127]. Results of various... 

Phillies, GDJ, Universal Scaling Equation for Self-Diffusion by Macromolecules in Solution, Macromolecules 19, 2367, 1986. 

H Moravettz, Macromolecules in solution Interscience Publishers, New Yormk,... 

Morawetz, H. (1975). Macromolecules in Solution, 2nd edn. Chapter 7. New York Wiley. 

Wu, C Laser Light Scattering Characterization of Special Intractable Macromolecules in Solution. Vol 137, pp. 103-134,... 

H. Morawetz, "Macromolecules in Solution", Second Edition, Wiley, New York, 1975, Chapter IX. 

Pervushin K, Riek R, Wider G, Wilthrich K. Attenuated T2 relaxation by mutual cancellation of dipole-dipole coupling and chemical shift anisotropy indicates an avenue to NMR structures of very large biological macromolecules in solution. Proc Natl Acad Sci 1997 94 12366-12371. 

JG Kirkwood, J Riseman. The intrinsic viscosities and diffusion constants of flexible macromolecules in solution. J Chem Phys 16 565-573, 1948. 

In the SEC mode, the separation occurs according to the molecular size of a macromolecule in solution, which is dependent on its chain length, chemical composition, solvent, and temperature. Thus, molecules of the same chain length but different composition may have different molecular sizes (hydrodynamic volumes). Since SEC separates according to hydrodynamic volume, SEC in different eluents can separate a copolymer in two diverging directions. This principle of... 

Grant, E. H., R. J. Shephard, and G. P. South. 1978. Dielectric Behaviour of Biological Macromolecules in Solution. Oxford, Clarendon Press. 

We consider a biological macromolecule in solution. Let X and Y represent the degrees of freedom of the solute (biomolecule) and solvent, respectively, and let U(X, Y) be the potential energy function. The thermal properties of the system are averages over a Boltzmann distribution P(X, Y) that depends on both X and Y. To obtain a reduced description in terms of the solute only, the solvent degrees of freedom must be integrated out. The reduced probability distribution P is... 

The characteristic feature of a macromolecule in solution is its high degree of conformational freedom. The simplest possible model for an isolated macromolecule is the random walk (or... 

Because the term microgel has the longest tradition and is most commonly used in polymer science and technology it is reasonable to accept it as the generic term for intramolecularly crosslinked macromolecules in solution, a state in which these species of macromolecules are usually handled and characterized. 

I first approached my theoretition friend and co-worker of many years, R. Simha, for statistical-mechanical assistance, and we obtained further the cooperation of H. Frisch, then just completing his Ph.D. at the Polytechnic Institute. The model we evolved was that of a macromolecule in solution colliding first with one of its segnents with a solvent-solid interface, becoming adsorbed when a complicated set of energetics becomes negative. 

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