Ogston theory

Rikvold and Stell [319,320,365] have developed an expression for the partition coefficient in a random two-phase medium made up of spherical particles. They found the partition coefficient to be essentially an exponential function of the solute radius, which is in qualitative agreement with the Ogston theory. 

To explain the selective reactivity of only one of the two identical groups, the Ogston theory further postulates that the reactivity is different at each of the points of attachment of the enzyme with the substrate. The three-point attachment theory thus explains how symmetrical organic molecules can be acted upon by an enzyme as if they presented a specific type of stereoisomerism. However, the absolute enzyme-substrate relationship remains unknown. In addition to citric acid, several other symmetrical substrates are known to be specifically oriented by their enzymes. 

Our purpose in this section is to derive a set of useful expressions for the chemical potentials starting with the principles of statistical mechanics. The expressions we shall obtain take the form of virial expansions similar to those of the Edmond and Ogston (6) but having a very different theoretical basis. Our model parameters are isobaric-isothermal virial coefficients which are about an order of magnitude smaller than the osmotic virial coefficients in the Edmond and Ogston model. We shall develop the theory neglecting the effect of polydispersity because we empirically did not find this to be very important at the level of accuracy commonly attainable in experimental phase diagrams for these systems. 

A theoretical treatment of aqueous two-phase extraction at the isoelectric point is presented. We extend the constant pressure solution theory of Hill to the prediction of the chemical potential of a species in a system containing soivent, two polymers and protein. The theory leads to an osmotic virial-type expansion and gives a fundamentai interpretation of the osmotic viriai coefficients in terms of forces between species. The expansion is identical to the Edmunds-Ogston-type expression oniy when certain assumptions are made — one of which is that the solvent is non-interacting. The coefficients are calculated using simple excluded volume models for polymer-protein interactions and are then inserted into the expansion to predict isoelectric partition coefficients. The results are compared with trends observed experimentally for protein partition coefficients as functions of protein and polymer molecular weights. 

In this paper we report preliminary work aimed at developing a comprehensive theory of protein partitioning. We focus attention on isoelectric partitioning and use statistical mechanics to examine the fundamental basis of the so called Edmonds-Ogston expression (3) and its extension to four component systems by King et ah (4). This expression,... 

The theory leads to an osmotic virial type expansion and gives a fundamental interpretation of the coefficients appeEiring in this expansion in terms of forces between the species. The expansion reduces to the Edmunds-Ogston expression only when certain assumptions are made -namely that the fluids are incompressible and that the solvent is... 

We have also shown that the Edmonds-Ogston expression and its extension by King, et are valid only if one assumes that the fluids are incompressible, that the solvent is non-interacting, and that Equations 28 and 29 are valid. The incompressibility assumption seems reasonable, but the lack of interaction between solvent and solutes seems less reasonable. We are currently investigating the consequences to the theory if this assumption is dropped. The assumption of the validity of Equations 28 and 29 is not a problem since these equations are valid when both species are flexible coils they are also valid in the case when one species is rigid and the other is a flexible coil. 

Bentley, R. Ogston and the development of prochirality theory. Nature 1978, 276, 673-676. 

Diagrammatic representation of the three point attachment theory of Ogston. X, Xj and X3 represent sites of attachment of citrate to the active center of aconitase. 

Early theories of hard sphere solute models, in chronological order of appearance, include the random-spheres pore model of Ogston (ref. 19), the... 

Besides the simplest model of cylindrical pores and rigid sphere molecules, theoretical treatments have been given for parallel, randomly positioned planes and/or randomly oriented planes models, with several types of molecular shape (ref. 10). However, these models still seem to be too artificial to be examined on an experimental basis. Interestingly enough, the Laurent Killander s model based on the Ogston s theory (ref. 35) (OLK model) should be counted as the most realistic version for polymeric gels, in the framework of Biddings et al (ref. 10). 

The findings supported the three point attachment theory that Ogston [77] had proposed precisely to explain the biological stereospecificity of symmetrical organic compounds. This concept will be best understood if one takes a three-dimensional view of the citric acid molecule. The reader should first be reminded that the carbon atom has four sp orbitals, and the angles between them are 109.5°. Thus, the forces represented by the valence bonds are symmetrically distributed around the center of the atom, and the angle that separates them is 109.5°. Consequently,... 

Ogston has recently put forward an idea which removes the difficulty of ascribing both reactions to one enzyme. It is a development of his theory discussed above of a three-point combination between enzyme and substrate. As already explained, the fumarate molecule in order to yield optically active malic acid must be so placed on the enzyme surface that only one double-bond component can react, but no direction need be exerted on the water in which H and OH are distributed. If it is now assumed that aconitase is constructed analogously to fumarase in that again no direction is exerted on the elements of water when they combine with aconitic acid, it is seen at once that two different compounds arise, namely, citric and isocitric acids. The occurrence of the reverse reaction would follow from the requirement of catalytic reversibility. 

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