Allosteric coefficient

This is an inverted parabolic relation in terms of ttx (calculated hydrophobic parameter of the substituents), which suggests that activity of these compounds first decreases as the hydrophobicity of substituents increases and after a certain point (inversion point ttx = 0.67), activity begins to increase. This may correspond to an allosteric reaction [54]. The indicator variable I is assigned the value of 1 and 0 for the presence and absence of N(CH3)2 substituent at the X position. Its positive coefficient suggests that the presence of a N(CH3)2 substituent at X position, increases the activity. REC is the relative effective concentration i.e., concentration relative to topotecan, whose value is arbitrarily assumed as 1, that is able to produce the same cleavage on the plasmid DNA in the presence of human topo I. 

Similar to generalized mass-action models, lin-log kinetics provide a concise description of biochemical networks and are amenable to an analytic solution, albeit without sacrificing the interpretability of parameters. Note that lin-log kinetics are already written in term of a reference state v° and S°. To obtain an approximate kinetic model, it is thus sometimes suggested to choose the reference elasticities according to simple heuristic principles [85, 89]. For example, Visser et al. [85] report acceptable result also for the power-law formalism when setting the elasticities (kinetic orders) equal to the stoichiometric coefficients and fitting the values for allosteric effectors to experimental data. 

For the irreversible reactions, we assume Michaelis Menten kinetics, giving rise to 15 saturation parameters O1. C [0, 1] for substrates and products, respectively. In addition, the triosephospate translocator is modeled with four saturation parameters, corresponding to the model of Petterson and Ryde-Petterson [113]. Furthermore, allosteric regulation gives rise to 10 additional parameters 7 parameters 9" e [0, — n for inhibitory interactions and 3 parameters 0" [0, n] for the activation of starch synthesis by the metabolites PGA, F6P, and FBP. We assume n = 4 as an upper bound for the Hill coefficient. 

For an enzyme with typical Michaelis-Menten kinetics, the value of e ranges from about 1 at substrate concentrations far below Km to near 0 as Vmax is approached. Allosteric enzymes can have elasticities greater than 1.0, but not larger than their Hill coefficients (p. 167). 

Not only can the concentration [EJ change but also allosteric effectors can alter the activity. Kacser and Bums defined this in temis of a controllability coefficient k,... 

Figure 22 Examples of enzyme kinetic plots used for determination of Km and Vmax for a normal and an allosteric enzyme Direct plot [(substrate) vs. initial rate of product formation] and various transformations of the direct plot (i.e., Eadie-Hofstee, Lineweaver-Burk, and/or Hill plots) are depicted for an enzyme exhibiting traditional Michaelis-Menten kinetics (coumarin 7-hydroxylation by CYP2A6) and one exhibiting allosteric substrate activation (testosterone 6(3-hydroxylation by CYP3A4/5). The latter exhibits an S-shaped direct plot and a hook -shaped Eadie-Hofstee plot such plots are frequently observed with CYP3A4 substrates. Km and Vmax are Michaelis-Menten kinetic constants for enzymes. K is a constant that incorporates the interaction with the two (or more) binding sites but that is not equal to the substrate concentration that results in half-maximal velocity, and the symbol n (the Hill coefficient) theoretically refers to the number of binding sites. See the sec. III.C.3 for additional details.

A fourth pattern of interaction (enzymes of group D) between allosteric activator and inhibitor is seen with barley endosperm. The ADPGIc PPase, which is poorly-activated by 3PGA, is inhibited by Pi (Table 4.2). However, 3PGA lowers (up to 3-fold) the S0 5 for ATP (i.e. the apparent affinity of ATP is increased) and the Hill coefficient.75 At 0.1 mM ATP, activation by 3PGA is about 4-fold 2.5 mM Pi reverses the effect. Thus, in barley endosperm, the prime effect of 3PGA or Pi may be to either increase or decrease the apparent affinity of the enzyme for the substrate, ATP. 

Show that this enzyme is indeed allosteric determine its cooperativity coefficient (Hill coefficient). Is the cooperativity positive, or is it negative What is K Is K equal to Km If not, why not When is K = Km ... 

Connectivity theorems allow to relate the control coefficients (systemic properties) to the elasticity coefficients (properties of the network s enzymes individually as if in isolation) (Westerhoff and Van Dam 1987 Heinrich and Schuster 1996 Fell 1997). The connectivity theorems have given us a strong insight into the functioning of metabolic pathways. For example, it follows directly from these theorems that enzymes that are very sensitive to the concentrations of metabolites, such as substrates, products and allosteric effectors, tend to have little control over the flux. This is illustrated by overproduction of phosphofructokinase in bakers yeast, an enzyme often referred to textbooks as rate-limiting. Yet, overproduction of phosphofructokinase does not lead to a significant flux increase, since the cell compensates by lowering the level of its allosteric effector fructose 2,6-bisphosphate (Schaaff et al. 1989 Davies and Brindle 1992). 

Once a protein structure has been solved, the study of the association of small molecules with the protein may be accomplished relatively easily by means of difference Fourier syntheses. The method has been widely applied in the study of binding of inhibitors and pseudo-substrates to a large number of proteins and has provided the means by which active and allosteric sites may be located. It is assumed that the small ligand does not change the unit cell or perturb the protein substantially, and that the protein phases are approximately equal to those for the protein and ligand. Small changes in conformation can be distinguished as in conventional difference syntheses. The coefficients used are... 

The structure revealed the basis for the pronounced allosteric nature of the enzyme. Initial rates of UDPGlcNAc isomerisation give a Hill coefficient [eqn. (5.20), Figure 5.5] of 2.29 and epimerisation of UDPManNAc does not take place except in the presence of its epimer. The asymmetric unit of the crystals of UDPGlcNAc 2-epimerase contains four copies of the enzyme arranged as two similar copies of the biological homodimer, with each dimer composed of one... 

An analysis of the influence of enzyme cooperativity in the mathematical model of product activated oscillatory glycolysis reaction was made by Goldbetter and Venieratos (1980). They established the relationship between the instabilities and the value of the Hill coefficient in the allosteric model for phosphofructokinase. 

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