Multiple Receptor Molecules

Given that the rate of convergence to the steady state of a complex system composed of two or more coupled subsystems is determined by the slowest subsystem (Strogatz 1994), the speed with which the probabilities Pij t) converge to their stationary values is determined by the minimum value of k nx + k and kyny + ky. When either nx or ny are equal to zero, Eqs. (6.18)-(6.21) reduce to the well-known Michaelis-Menten equation that we found in Chap. 5 while studying the enzyme-substrate interaction. 

To understand Eq. (6.22) take a look at the reactions in Eqs. (6.1)-(6.4). The first two terms on the right-hand side of Eq. (6.22) correspond to the forward reaction in (6.1) the first term accounts for the case in which one of such reactions takes the system into the state ( r, wra , r), while the second term considers the reactions that take the system out of this state. In a similar way, the third and fourth terms on the right-hand side of Eq. (6.22) correspond to the backward reaction in (6.1), the fifth and sixth terms correspond to the forward reaction in (6.2), and so forth for the rest of the reactions. 

The reader can imagine how difficult it is to solve Eq. (6.22) directly. However, one can construct its solution from Eqs. (6.11)-(6.14)—with Px(jt) and / y(t) as given by Eqs. (6.15) and (6.16)—and from the supposition that all the r receptor molecules are independent from each other. In summary, given that we know the probability distribution for all the states of a single molecule, the probability distribution for the nj molecules is nothing but a multinomial distribution  

With the probability distribution it is possible to calculate the average number of molecules in each state  

At this point we make use of the multinomial distribution properties (Evans et al. 2000) to obtain 

---

Most effective differentiation of the receptor between substrates will occur when multiple interactions are involved in the recognition process. The more binding regions (contact area) present, the stronger and more selective will be the recognition (17). This is the case for receptor molecules that contain intramolecular cavities, clefts or pockets into which the substrate may fit (Fig. 1). 

In this type of arrays, microbeads carrying different indicator or receptor molecules are randomly loaded into the wells of chemically etched optical fiber or silicon chips [89, 90, 100] (Fig. 6b). The beads are encoded with single or multiple luminescent indicators or labels embedded into the polymeric core and/or bound... 

M. W. Hosseini, A. J. Blacker, and J.-M. Lehn, Multiple molecular recognition and catalysis, nucleotide binding and ATP hydrolysis by a receptor molecule bearing an anion binding site, an intercalator group, and a catalytic site, J. Chem. Soc., Chem. Commun. 596(1988). 

Though naturally occurring peptides based on coded amino acids have been widely used as drugs, there are problems with the use of peptides as therapeutic agents. The problems mainly arise from their rapid metabolism by proteolysis, and their interactions at multiple receptors. As a result, peptide researchers have sought modifications of peptide structures to create more stable and bioavailable molecules. P-27 ... 

Inclusion of guest species in dendritic host molecules 6.2.3.1 Dendrimers with multiple receptor units... 

Although the above discussion focused on the binding of small molecules to biopolymers, similar issues arise in connection with the binding of biopolymers to one another. In particular, rapid motion (times of a few nanoseconds) of surface loops of proteins may facilitate the assembly of chaperonins [16] and allow the binding of multiple receptors in the case of certain fibronectin domains [4]. 

A small number of ancestral proteins encoded by ancestral genes may have given rise to a multiplicity of active peptides in concert with the evolution of complementary receptor molecules. Our current knowledge of insect neuropeptides is consistent with and actually supports these views. 

---