Linear receptors

Suppose now that the sites are not independent, but that addition of a second (and subsequent) ligand next to a previously bound one (characterized by an equilibrium constant K ) is easier than the addition of the first ligand. In the case of a linear receptor B, the problem is fonnally equivalent to the one-dimensional Ising model of ferromagnetism, and neglecting end effects, one has [M] ... 

Figure 3.16 Imine oligomers used as building blocks and rod-shaped guest used to amplify a linear receptor.

The second application of the CFTI approach described here involves calculations of the free energy differences between conformers of the linear form of the opioid pentapeptide DPDPE in aqueous solution [9, 10]. DPDPE (Tyr-D-Pen-Gly-Phe-D-Pen, where D-Pen is the D isomer of /3,/3-dimethylcysteine) and other opioids are an interesting class of biologically active peptides which exhibit a strong correlation between conformation and affinity and selectivity for different receptors. The cyclic form of DPDPE contains a disulfide bond constraint, and is a highly specific S opioid [llj. Our simulations provide information on the cost of pre-organizing the linear peptide from its stable solution structure to a cyclic-like precursor for disulfide bond formation. Such... 

The two /3-turn structures, pc and Pe are the most stable among those considered. This is in accord with the unconstrained nanosecond simulations of linear DPDPE, which converged to these conformers [14]. Because the cyclic form is relatively rigid, it is assumed that the conformation it adopts in solution is the biologically active one, responsible for its high affinity and specificity towards the 5 opioid receptor. The relatively low population of the cyclic-like structure for the linear peptide thus agrees qualitatively with the... 

The second application of the CFTI protocol is the evaluation of the free energy differences between four states of the linear form of the opioid peptide DPDPE in solution. Our primary result is the determination of the free energy differences between the representative stable structures j3c and Pe and the cyclic-like conformer Cyc of linear DPDPE in aqueous solution. These free energy differences, 4.0 kcal/mol between pc and Cyc, and 6.3 kcal/mol between pE and Cyc, reflect the cost of pre-organizing the linear peptide into a conformation conducive for disulfide bond formation. Such a conformational change is a pre-requisite for the chemical reaction of S-S bond formation to proceed. The predicted low population of the cyclic-like structure, which is presumably the biologically active conformer, agrees qualitatively with observed lower potency and different receptor specificity of the linear form relative to the cyclic peptide. 

Two fundamental questions have emerged from these studies, ie, to what extent are agonists and antagonists binding similarly or differendy to the respective receptors, and can inhibitory compounds be developed that are active in vivo in humans as well as in vitro. An oxytocia antagonist that can block premature uterine contractions presents a promising example of the clinical utihty of such stmctures (47). Both linear as well as bicycHc modifications of these hormones also have provided new antagonist stmctures. 

Using the Gaussian plume model and the other relations presented, it is possible to compute ground level concentrations C, at any receptor point (Xq, in the region resulting from each of the isolated sources in the emission inventory. Since Equation (2) is linear for zero or linear decay terms, superposition of solutions applies. The concentration distribution is available by computing the values of C, at various receptors and summing over all sources. 

The basis of this model is the experimental fact that most agonist dose-response curves are hyperbolic in nature. The reasoning for making this assumption is as follows. If agonist binding is governed by mass action, then the relationship between the agonist-receptor complex and response must either be linear or hyperbolic as well. Response is thus defined as... 

This is a linear relation often referred to as the Cheng-Prusoff relationship [5], It is characteristic of competitive ligand-receptor interactions. An example is shown in Figure 4.6b. 

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