Cooperativity thermodynamics

Pan,J., Thirumalai, D., and Woodson, S. A. (1999). Magnesium-dependent folding of selfsplicing RNA Exploring the link between cooperativity, thermodynamics, and kinetics. 

Phase transitions are typically described in the canonical ensemble with the temperatnre kept fixed. This is also natural from an experimentalist s point of view, since the temperature is a convenient external control parameter. The macrostates are weighted according to the Boltzmann distributionpcg, E) g(E) exp(—A nice feature of the canonical ensemble is that the temperature dependence of fluctuations of thermodynamic quantities is usually a very useful indicator for phase or pseudophase transitions. This cooperative thermodynamic activity is usually indicated by peaks or, in the thermodynamic limit (if it exists), by divergences of these fluctuations. Even for small systems, peak temperatures can frequently be identified with transition temperatures. 2 lthough in these cases peak temperatures typically depend on the fluctuating quantities considered, in most cases associated pseudophase transitions are doubtless manifest. 

E. F. Vainstein Department of Kinetics and Thermodynamics of Cooperative Processes, N. M. Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Moscow, Russia... 

The theory of linked functions establishes the general thermodynamic meaning of the cooperative behavior of the system. On the basis of Hill s equation,... 

The relationship of thermodynamic functions of selective bonding of Hb to a series of carboxylic CP in the variation of the degree of ionization of carboxylic groups is expressed by the effect of enthalpy-entropy compensation (Fig. 18). The compensation effect of enthalpy and entropy components is the most wide-spread characteristic of many reactions in aqueous solutions for systems with a cooperative change in structure [78],... 

Thermodynamic Aspects of the Triple Helix-Coil Transition 4.1 Cooperative Processes... 

For this kind of cooperative processes, it is characteristic that the formation of the nucleus is thermodynamically more difficult than for further propagation steps (positive cooperativity). This implies that the elementary transition step of an individual chain segment (tripeptide unit) is influenced by the state of adjacent segments through intramolecular interactions. 

The stability of a trivial assembly is simply determined by the thermodynamic properties of the discrete intermolecular binding interactions involved. Cooperative assembly processes involve an intramolecular cyclization, and this leads to an enhanced thermodynamic stability compared with the trivial analogs. The increase in stability is quantified by the parameter EM, the effective molarity of the intramolecular process, as first introduced in the study of intramolecular covalent cyclization reactions (6,7). EM is defined as the ratio of the binding constant of the intramolecular interaction to the binding constant of the corresponding intermolecular interaction (Scheme 2). The former can be determined by measuring the stability of the self-assembled structure, and the latter value is determined using simple monofunctional reference compounds. 

The value of EM for a cooperative self-assembled structure provides a measure of the monomer concentration at which trivial polymeric structures start to compete, and therefore EM represents the upper limit of the concentration range within which the cooperative structure is stable (Scheme 2). The lower limit of this range is called the critical self-assembly concentration (csac) and is determined by the stoichiometry of the assembly and the strength of the non-covalent binding interactions weaker interactions and larger numbers of components raise the csac and narrow the stability window of the assembly (8). Theoretical treatments of the thermodynamics of the self-assembly process have been reported by Hunter (8), Sanders (9), and Mandolini (10). The value of EM is lowered by enthalpic contributions associated with... 

In the above section, we have shown that the whole apparatus of a cell is organised by thermodynamic and kinetic constraints on concentrations of all its chemical components. We know, in fact, that individually and cooperatively the organic and inorganic molecules and ions are controlled in a cell in a given state provided that external conditions of material and energy availability are fixed. This is known as a homeostatic steady state and not an equilibrium condition. Now there are two kinds of constraints, which we mentioned in Chapter 3. The first is equilibrium, which applies when combinations of components are in balanced concentration with their free entities... 

Such internal thermodynamic equilibria where A is a protein are found for non-metal components, including free coenzymes and substrates where B is a small molecule, or where free M is an ion of either a non-metal, e.g. Cl" or HCOj, or a metal, e.g. K+ or Mg2+, or is H+, and they are involved in, even necessary for, catalysis, pumping and cooperative controls of many metabolic paths. All such combinations reach equilibrium, as long as exchange is fast, where a fast rate can be taken as, say, 10-3 s for dissociation in cells. Note that equilibria with defined binding constants for AB or AM formation in any system reduce the number of variables and hence AB and AM concentrations are defined by those of free A, B and M, leaving two independent variables for each equilibrium. In some cases, the... 

T. K. Dam, R. Roy, D. Page, and C. F. Brewer, Negative cooperativity associated with binding of multivalent carbohydrates to lectins. Thermodynamic analysis of the multivalency effect Biochemistry, 41 (2002) 1351-1358. 

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