Sequential interaction model

Enzyme activity can also be affected by binding of substrate and nonsubstrate Mgands, which can act as activators or inhibitors, at a site other than the active site. These enzymes are called allosteric. These responses can be homotropic or heterotropic. Homotropic responses refer to the allosteric modulation of enzyme activity strictly by substrate molecules heterotropic responses refer to the allosteric modulation of enzyme activity by nonsubstrate molecules or combinations of substrate and nonsubstrate molecules. The allosteric modulation can be positive (activation) or negative (inhibition). Many allosteric enzymes also display cooperativity, making a clear differentiation between allosterism and cooperativity somewhat difficult. 

Cooperative substrate binding results in sigmoidal v versus [S] curves (Fig. 8.1). The Michaelis-Menten model is therefore not appMcable to cooperative enzymes. Two major equihbrium models have evolved to describe the catalytic behavior of cooperative enzymes the sequential interaction and concerted transition models. The reader should be aware that other models have also been developed, such as equilibrium association-dissociation models, as well as several kinetic models. These are not discussed in this chapter. 

---

Two major models for allosteric enzymes have been proposed. These are the sequential interaction model and the concerted-symmetry ... 

Figure 4-50 The sequential interaction model of allosteric enzymes. As each site is occupied, the subunit carrying the site undergoes a change from the A conformation to the B conformation. As a result, new interactions between subunits are established and the affinities of the vacant sites change. K represents a dissociation constant. Thus, if the affinities of vacant sites increase, a, b, and c (the interaction factors) are <1 and we observe positive cooperativity (a sigmoidal velocity curve). The sequential interaction model also provides for, negative cooperativity (a, b, and c are > ). (o ) Dimer model. The two ways of arranging S to form a singly-occupied species is shown, (fe) Tetramer model. For simplicity, only one arrangement of each occupied species is shown.

Fipire 4- 4 According to the concerted-symmetry model, an allosteric inhibitor binds preferendaliy to the T form. This causes the velocity curve to become more sigmoidal tvith a higher [S]gj. An allosteric activator mimics the substrate by binding preferentially to the R form. As a result, the velocity curve becomes less sigmoidal (hyperbolic at saturating activator) and fS]oi decreases. These observations can also be explained in terms of the sequential interaction model. 

An allosteric dimer has an interaction factor, a, of 0.2 when analyzed according to the sequential interaction model (i.e., the binding of the first molecule of S increases the binding constant of the vacant site by a factor of 5—the dissociation constant of the vacant site decreases to 0.2 of the original value), (a) What is the relative distribution of enzyme species at [S] = 0.3 Ks (b) What is the specific velocity at [S] = 0.3 Ks (c) Will the calculated value of n,pp equal 2 ... 

From the binding sequences in reaction (13.79), we can see that the general KNF model takes into account a variety of possible subunit interactions that are able to affect affinities of vacant sites. Therefore, the general KNF model is far more versatile than the simple sequential interaction model or, for that matter, than the MWC model. 

The simple sequential interaction model is more general than the concerted-symmetry model in that there are many combinations of values for a, b, and c, for which there are no equivalent values of L and c. Furthermore, the... 

The MWC concerted-symmetry and KNF sequential interaction models may be considered as extreme cases of the more general model shown in Fig. 19. A general model for a four-site allosteric enzyme involves the hybrid oligomers. The first and the fourth column in Fig. 19 represent the concerted-symmetry model. The diagonal represents the sequential interaction model. As shown, there are 25 different types of enzyme forms. If the potential nonequivalent complexes are included (such as, e.g., two different T3RS2), the number raises to 44 possible enzyme forms (Hammes Wu, 1971). 

The H NMR spectral changes of the abnormal ferric 0 chains of Hb M Milwaukee on oxygenation of the normal deoxy a chains are not compatible with a two-structure model for cooperativity and support the concept of direct ligand-linked interactions between subunits embodied in a sequential-type model (Fung et al., 1976, 1977). 

Chemometrics has been defined in some texts [155] as the entire process whereby data are transformed into information used for decision-making. It is this definition that is the most applicable to separation sciences, more specifically in method development and optimisation in liquid chromatography. In this example, chemometrics has been used to predict optimum separation conditions based on empirical data and other separation information. Chemometric approaches to method development can be based on either sequential simplex models [156] or simultaneous fixed factorial designs [157] or interactive mixture designs [158] which combine the advantages of simultaneous and simplex models. 

We propose a sequential ionization model to include the effects of ionization of Ceo during the interaction with laser pulses. In this model, Cgo is assumed to be vertically ionized to Cfo when the instantaneous light intensity I t) reaches... 

The basic premise of the sequential interaction (SI) model is that significant changes in enzyme conformation take place upon substrate binding, which result in altered substrate binding affinities in the remaining active sites (Fig. 8.2). For the case of positive cooperativity, each substrate molecule that binds makes it easier for the next substrate molecule to bind. The resulting v versus [S] curve therefore displays a marked slope increase as a function of increasing substrate concentration. Upon saturation of the... 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

This concerted model assumes furthermore that the symmetry of the molecule is conserved so that the activity of all its subunits is either equally low or equally high, that is, all structural changes are concerted. Subsequently Daniel Koshland, University of California, Berkeley, postulated a sequential model in which each subunit is allowed independently to change its tertiary structure on substrate binding. In this model tertiary structural changes in the subunit with bound ligand alter the interactions of this... 

A common feature in the models reviewed above was to calculate pressure and temperature distributions in a sequential procedure so that the interactions between temperature and other variables were ignored. It is therefore desirable to develop a numerical model that couples the solutions of pressure and temperature. The absence of such a model is mainly due to the excessive work required by the coupling computations and the difficulties in handling the numerical convergence problem. Wang et al. [27] combined the isothermal model proposed by Hu and Zhu [16,17] with the method proposed by Lai et al. for thermal analysis and presented a transient thermal mixed lubrication model. Pressure and temperature distributions are solved iteratively in a iterative loop so that the interactions between pressure and temperature can be examined. 

The formation of the PIC described above is based on the sequential addition of purified components in in vitro experiments. An essential feature of this model is that the assembly takes place on the DNA template. Accordingly, transcription activators, which have autonomous DNA binding and activation domains (see Chapter 39), are thought to function by stimulating either PIC formation or PIC function. The TAF coactivators are viewed as bridging factors that communicate between the upstream activators, the proteins associated with pol II, or the many other components of TFIID. This view, which assumes that there is stepwise assembly of the PIC—promoted by various interactions between activators, coactivators, and PIC components— is illustrated in panel A of Figure 37-10. This model was supported by observations that many of these proteins could indeed bind to one another in vitro. 

The solution phase is modeled explicitly by the sequential addition of solution molecules in order to completely fill the vacuum region that separates repeated metal slabs (Fig. 4.2a) up to the known density of the solution. The inclusion of explicit solvent molecules allow us to directly follow the influence of specific intermolecular interactions (e.g., hydrogen bonding in aqueous systems or electron polarization of the metal surface) that influence the binding energies of different intermediates and the reaction energies and activation barriers for specific elementary steps. 

---