Subunits, interacting

We conclude this section by adding one more type of interaction that will appear in some models discussed in this book. These are interactions between subunits in a multisubunit model for adsorbent molecules. The subunit-subunit interaction will in general depend on the conformational states of the subunit. For instance, two subunits in states a, P will be assigned interaction energy E. As with ligand- ligand interaction, subunit-subunit interaction is modified when we average over all states of the subunits. 

Many proteins consist of a single polypeptide chain, and are defined as monomeric proteins. However, others may consist of two or more polypeptide chains that may be structurally identical or totally unrelated. The arrangement of these polypeptide subunits is called the quaternary structure of the protein. [Note If there are two subunits, the protein is called dimeric , if three subunits trimeric , and, if several subunits, multimeric. ] Subunits are held together by noncovalent interactions (for example, hydrogen bonds, ionic bonds, and hydrophobic interactions). Subunits may either function independently of each other, or may work cooperatively, as in hemoglobin, in which the binding of oxygen to... 

Even though in vitro experiments necessarily remove biomolecules from the cellular environment, the structures and dynamics of individual macromolecules provide insights to their biological functions. For example, structural studies have revealed that the protein hemoglobin is made up of four interacting subunits, two a subunits and two ft subunits. Furthermore, each subunit has two distinct conformational states, called the R state and the T state, and the energy of interaction between two neighboring subunits in different states is different from that of two subunits in the same state. This phenomenon is the structural basis of the observed allosteric... 

Mammalian ferritins are heteropolymers of H- and L-chains. These subunits are very closely related, with an a-carbon rmsd of 0.5 A and 55% sequence identity conservation of primary sequence rises to 79% when considering those residues responsible for intersubunit interactions. Subunit assembly appears to take place via partially structured monomers associating to form fully structured homodimers, which then aggregate further. Upon chemical denaturation and refolding, heterodimers are rarely observed. ... 

A functional system is best described as a collection of a distinct number of interacting subunits forming a new entity with specific properties. The subunits are hierarchically organized on different levels of complexity, leading to new qualities of the functional system that cannot be achieved by uncontrolled combination of the snbunits. 

There are a number of ways of monitoring the distribution of electron density in any molecular entity. The total density can be computed at a number of points in space and presented as a contour map or some three-dimensional representation. Shifts are easily examined by density difference maps which plot the difference in density between two different configurations. For example, the density shifts caused by H-bond formation can be taken as the difference between the complex on one hand, and the sum of the densities of the two non interacting subunits on the other, with the two species placed in identical positions in either case. Comparisons with x-ray diffraction data have verified the validity of this ap-proach. Also, the total density of the complex itself can be examined for the presence of critical points that indicate H-bonding interactions . 

In a subsequent paper Brant and Flory (55) have successfully correlated their experimental data with polypeptide chain structure using the rotational-isomeric state model and statistical mechanical methods applicable to linear systems of interacting subunits. 

Fig. 27. Illustration of the binding change mechanism for ATP synthesis by the proton-translocating ATP synthase. F, has three chemically identical but conformationally distinct Interacting subunits designated as 0" [open], "L" [loose] and "T [tight] see text forfurfher details on how the three catalytic [ap] sites pass through three conformational states driven by proton flux. Figure modeled after Cross (1981) The mechanism and reguiation of ATP synthesis by F -ATPases. Annu Rev Biochem 50 687.

Extension of these ideas to those more relevant to organic chemistry requires other examples 1.) introduction of polarity into the bond, as in CHj—which is still ditopic 2.) introduction of the aromatic chromophore, as in PhCH2— NHs, which is still ditopic at the reactive sigma bond but provides an interactive subunit, the aromatic ring and 3.) a system of higher topicity,... 

The last criterion of the decision tree is the shape complementarity between the two interacting subunits within the cavity. The less favorable case is when both chains are densely packed and make many direct interactions within the cavity. As already mentioned, inhibitors should mimic the natural substrate but in addition they should make additional contacts that help enhance their potency. The cavity should therefore contain atoms that are not directly engaged in the interaction between the two proteins such that it is possible to design molecules that interact directly with them. Interfaces that possess... 

Theories of interacting subunits are often referred to as allosteric theories, but the use of this word is unfortunate and should be avoided. The word allostery (Greek alios, other stereos, solid) refers to the possibility that substances (known as modifiers or effectors) can be attached at sites other than the site for the attachment of substrate. This is a completely different type of phenomenon and is of great importance in connection with the regulation of metabolic processes, but should be sharply distinguished from subunit interactions. However, in some enzymes the two effects are found together. 

Allosteric activators and inhibitors (allosteric effectors) are compounds that bind to the allosteric site (a site separate from the catalytic site) and cause a conformational change that affects the affinity of the enzyme for the substrate. Usually an allosteric enzyme has multiple interacting subunits that can exist in active and inactive conformations, and the allosteric effector promotes or hinders conversion from one conformation to another. 

The nonlinearity of kinetic equations of the Hodgkin-Huxley type might also result, at least in part, from the cooperative allosteric properties of ion channels. The crystallographic study of these channels indeed reveals that they are often formed by multiple interacting subunits (Noda et al, 1984). 

VI. Characterization of Interacting Subunits and Dissection OF Interaction Domains... 

Two types of phenomena are responsible for such regulatory properties of enzymes. First are the cooperative phenomena in proteins and enzymes, and second are the allosteric properties of proteins and enzymes (Kurganov, 1982). Cooperativity is the apparent change in affinity or activity-that deviates from Michaelis-Menten kinetics-of an enzyme or protein with its substrate or other ligand as the concentration of the ligand changes. Cooperativity often requires that the enzyme or protein is built up of interacting subunits, but may also arise... 

To represent the interaction between subunits of different conformational stmcture, the interaction constants, Kaai Kbb wiU be employed in this connection, it will he assumed that Kaa = i. Kab and Kbb are defined by Eqs. (13.74) and (13.75) in which (AB) refers to interacting subunits, whereas (A) and (B) refer to noninteracting subunits ... 

The origin of optical activity in molecules often reduces to the question of how the molecule acquires the electronic properties expected of a chiral object when it is formed from an achiral object. Most often an achiral molecule becomes chiral by chemical substitution. In coordination compounds, chirality commonly arises by the assembly of achiral units. So it is natural to develop ideas on the origins of chiral spectroscopic properties from the interactions of chirally disposed, but intrinsically achiral, units. Where this approach, an example of the independent systems model, can be used, it has obvious economic benefits. Exceptions will occur with strongly interacting subunits, e.g., twisted metal-metal-bonded systems, and in these cases the system must be treated as a whole—as an intrinsically chiral chromophore. ... 

With the most advanced streptavidin variants, the strategy in which a racemic catalyst is converted to a chiral-at-metal complex and then further assisted by residues in the chiral protein has led to the development of both R- and 5-selective synthetic enzymes for imine reduction. Extensive kinetic data has been obtained for these new synthetic enzymes, and computer modelling of the complex stmctures (which contain four interacting subunits) serves to support and understand the results. An induced lock and key where the host protein structure determines the catalyst structure and the reduction selectivity is proposed (Fig. 44) [141]. 

Broadening the scope, we may briefly consider a nonexhaustive panorama of various types and features of supramolecular polymers depending on their constitution, characterized by three main parameters the nature of the core/framework of the monomers, the type of noncovalent interaction(s), and the eventual incorporation of functional subunits. The interactions may involve complementary arrays of hydrogen-bonding sites, electrostatic forces, electronic donor-acceptor interactions, metalion coordination, etc. The polyassociated structure itself may be of main-chain, side-chain, or branched, dendritic type, depending on the number and disposition of the interaction subunits. The central question is that of the size and the polydispersity of the polymeric supramolecular species formed. Of course their size is expected to increase with concentration and the polydispersity depends on the stability constants for successive associations. The dependence of the molecular weight distribution on these parameters may be simulated by a mathematical model [19]. These features are detailed in Chapters 2, 3, and 6 for various growth mechanisms. 

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