The [T.sub.M] [pK.sub.a] and cooperativity of the pH driven folding (Hill coefficient
) were similarly determined from fitting of the Hill equation  using the ECD signal obtained at 298 nm plotted versus pH.
is a monotonically increasing function  in which [n.sub.j] is the Hill coefficient
, [[beta].sub.j] is a positive constant, and [k.sub.j] is the apparent dissociation constant derived from the law of mass action, which equals the ratio of the dissociation rate of the ligand-receptor complex to its association rate.
where [M.sub.i] denotes the concentrations of three mRNA and [N.sub.i] denotes the concentrations of three repressor-proteins, [[alpha].sub.i] is the feedback regulation coefficient, [[beta].sub.i] denotes the ratio of the protein decay rate to the mRNA, and H is the Hill coefficient
, i = lacl, tetR, cl; j = cl, lacl, tetR.
Firstly the values for [ED.sub.50], maximum effect ([E.sub.max]) and Hill coefficient
(h) were determined by non-linear regressions of the dose--response curves (for each drug and mixtures), fixing zero as the minimal effect ([E.sub.min]).
In order to further explore whether the interactions between warfarin and HSA occur and the influence of ferulic acid on them, we primarily focus on investigating the effect of warfarin on fluorescence spectrum of HSA, fluorescence quenching mechanism, binding constant, Hill coefficient
, binding mode, and the effect of different ferulic acid concentrations on the binding, which are expected to provide more information about the interaction between warfarin and HSA.
Capsaicin, the reference agonist of TRPV1, and piperine caused a concentration-dependent response in PC-3 cells, achieving maximal effect at [10.sup.-5] and [10.sup.-3] M, respectively, with similar [F.sub.max] (204.8 [+ or -] 184.3% piperine versus 176.6 [+ or -] 35.83% capsaicin, P = 0.8814) and Hill coefficient
(0.70 [+ or -] 0.50 piperine versus 1.59 [+ or -] 0.86 capsaicin, P = 0.3752) and not significantly different [EC.sub.50] (4.14 x 10-4 M piperine versus 1.90 x [10.sup.-6] M capsaicin, P = 0.0675).
On the other hand, the Hill equation requires just one parameter (the Hill coefficient
) in addition to those required by the corresponding non-cooperative equation.
where S stands for the variable substrate, VJ is the maximal velocity observed under the conditions used, if is the cooperativity parameter (Hill coefficient
), and the constant [K.sup.n.sub.0.5] denotes the substrate concentration at which the reaction rate is half of the maximal rate.
1D); the Hill coefficient
of 1.9 suggests that the binding of at least two molecules of quinine are required to produce the effect.
Hb samples incubated with GSH for 4 and 7 days were 56.9% and 79.2% glutathionylated, respectively, and exhibited 1.9- and 2.5-fold increases in oxygen affinity, and 0.72- and 0.67-fold decreases in the Hill coefficient
, respectively, compared with Hb incubated without GSH.
When phosphorylation and dephosphorylation of p53 are considered separately, a near-optimal switch is possible via Hill equation, where the Hill coefficient
equals the number of phosphorylation sites .
where [I.sub.drug] is the end-of-pulse current in the presence of drug, [I.sub.control] is the end-of-pulse current in the absence of drug, [drug] is the extracellular drug concentration, [K.sub.d] is the apparent dissociation constant and n is the Hill coefficient