A Hierarchical Approach to Cooperativity in Macromolecular and Self-Assembling Binding Systems

Abstract

The study of complex macromolecular binding systems reveals that a high number of states and processes are involved in their mechanism of action, as has become more apparent with the sophistication of the experimental techniques used. The resulting information is often difficult to interpret because of the complexity of the scheme (large size and profuse interactions, including cooperative and self-assembling interactions) and the lack of transparency that this complexity introduces into the interpretation of the indexes traditionally used to describe the binding properties. In particular, cooperative behaviour can be attributed to very different causes, such as direct chemical modification of the binding sites, conformational changes in the whole structure of the macromolecule, aggregation processes between different subunits, etc. In this paper, we propose a novel approach for the analysis of the binding properties of complex macromolecular and self-assembling systems. previous work, it was shown that K c could be decomposed as an average of equilibrium constants in two ways: intrinsic constants for Adair binding systems and elementary constants for the general case. In this study, we show that these two decompositions are particular cases of a more general expression, where the average is over partial association quotients, associated with subsystems from which the system is composed. We also show that if the system is split into different subsystems according to a binding hierarchy that starts from the lower, microscopic level and ends at the higher, aggregation level, the global association quotient can be decomposed following the hierarchical levels of macromolecular organisation. In this process, the partial association quotients of one level are expressed, in a recursive way, as a function of the partial quotients of the level that is immediately below, until the microscopic level is reached. As a result, the binding properties of very complex macromolecular systems can be analysed in detail, making the mechanistic explanation of their behaviour transparent. In addition, our approach provides a modelindependent interpretation of the intrinsic equilibrium constants in terms of the elementary ones.

Cooperativity in Noncovalent Interactions

“…The quantification of cooperativity differs based on the approach and the nature of the system employed. − …”

“…Measures of cooperativity based on a combination of mathematical modeling and experimental data are available in few studies. ,,,− Mariuzza and co-workers used surface plasmon resonance techniques along with modeling on a trimolecular protein complex as a model system for quantifying cooperativity . The complex considered in this instance was obtained by the simultaneous interaction of a superantigen with major histocompatibility complex and T cell receptor.…”

“…The cooperative character of the spin-crossover in these materials was quantified using the so-called Slichter and Drickamer and domain models based on data obtained from differential scanning calorimetry. Mas and co-workers have emphasized the hierarchical approach to cooperativity in macromolecular and self-assembling binding systems . A global association quotient which was defined as K c = [occupied sites]/([free sites] L ), with L being the free ligand concentration was employed.…”

Using competition assays to quantitatively model cooperative binding by transcription factors and other ligands

“…Any specific binding model can be related to the terms and parameters of the binding polynomial. Some authors have introduced theoretically and pedagogically useful formalism into the binding polynomial, which aid in relating the general parameters to specific binding models [8][9][10][11].…”

The ‘Densitometric Image Analysis Software’ and Its Application to Determine Stepwise Equilibrium Constants from Electrophoretic Mobility Shift Assays

“…One way to quantify protein-DNA binding is by using a curve-fitting approach [4] , [7] – [9] . However, curve-fitting only provides binding parameter values, no standard deviations.…”