Mutation stability

For instance, if we wish to have sequences with some value of the latent heat Nq (that is, q per monomer), these sequences should deliver ground state as low as Eg Nq, which means that the fraction of such sequences should be proportional to fF( lp Nq)ortoexp[ Nq 2s/A]. These same sequences exhibit also mutation stability and environmental stability, all governed by the same energy scale Nq. Thus, only an exponentially small fraction of all sequences are protein-like in the sense of all these properties (latent heat, stability, etc). To find and select protein-like sequences is a hard work indeed But the total number of sequences is also exponentially large, say, = exp [AflnQ], where Q is the number of monomer species... 

CAN MUTATIONS STABILIZE STRUCTUREOF AN ENZYMETO ENVIRONMENTAL CONDITIONS ... 

In Figure 7b, the data are plotted as AG yielding a linear function. Extrapolation to 2ero denaturant provides a quantitative estimate of the intrinsic stability of the protein, AG, which in principle is the free energy of unfolding for the protein in the absence of denaturant. Comparison of the AG values between mutant and wild-type proteins provides a quantitative means of assessing the effects of point mutations on the stability of a protein. 

Lys-12, which lies close to the active site, and the role of this residue is the stabilization of the enediolate. This explicitly explains the inactivity of a Lys-12 to Met mutation [61]. 

We know much more about factors that influence the stability of the native state, mainly from experiments using directed mutations in proteins of known three-dimensional structure. Such experiments have yielded... 

Thirty percent of the tumor-derived mutations are in L3, which contains the single most frequently mutated residue, Arg 248. Clearly the interaction between DNA and the specific side chain of an arginine residue inside the minor groove is of crucial importance for the proper function of p53. It is an open question whether this interaction is needed for the recognition of specific DNA sequences, or is required for the proper distortion of the DNA structure, or a combination of both. Other residues that are frequently mutated in this region participate in interactions with loop L2 and stabilize the structures of loops L2 and L3. Mutations of these residues presumably destabilize the structure so that efficient DNA binding can no longer take place. 

The single mutation Asp 32-Ala reduces the catalytic reaction rate by a factor of about lO compared with wild type. This rate reduction reflects the role of Asp 32 in stabilizing the positive charge that His 64 acquires in the transition state. A similar reduction of kcat and kcat/ m (2.5 x 10 ) is obtained for the single mutant Asn 155-Thr. Asn 155 provides one of the two hydrogen bonds to the substrate transition state in the oxyanion hole of subtilisin. 

The catalytic triad consists of the side chains of Asp, His, and Ser close to each other. The Ser residue is reactive and forms a covalent bond with the substrate, thereby providing a specific pathway for the reaction. His has a dual role first, it accepts a proton from Ser to facilitate formation of the covalent bond and, second, it stabilizes the negatively charged transition state. The proton is subsequently transferred to the N atom of the leaving group. Mutations of either of these two residues decrease the catalytic rate by a factor of 10 because they abolish the specific reaction pathway. Asp, by stabilizing the positive charge of His, contributes a rate enhancement of 10. ... 

The oxyanion binding site stabilizes the transition state by forming two hydrogen bonds to a negatively charged oxygen atom of the substrate. Mutations that prevent formation of one of these bonds in subtilisin decrease the rate by a factor of about 10. ... 

Glycine residues have more conformational freedom than any other amino acid, as discussed in Chapter 1. A glycine residue at a specific position in a protein has usually only one conformation in a folded structure but can have many different conformations in different unfolded structures of the same protein and thereby contribute to the diversity of unfolded conformations. Proline residues, on the other hand, have less conformational freedom in unfolded structures than any other residue since the proline side chain is fixed by an extra covalent bond to the main chain. Another way to decrease the number of possible unfolded structures of a protein, and hence stabilize the native structure, is, therefore, to mutate glycine residues to any other residue and to increase the number of proline residues. Such mutations can only be made at positions that neither change the conformation of the main chain in the folded structure nor introduce unfavorable, or cause the loss of favorable, contacts with neighboring side chains. 

Both types of mutations have been made in T4 lysozyme. The chosen mutations were Gly 77-Ala, which caused an increase in Tm of 1 °C, and Ala 82-Pro, which increased Tm by 2 °C. The three-dimensional structures of these mutant enzymes were also determined the Ala 82-Pro mutant had a structure essentially identical to the wild type except for the side chain of residue 82 this strongly indicates that the effect on Tm of Ala 82-Pro is indeed due to entropy changes. Such effects are expected to be additive, so even though each mutation makes only a small contribution to increased stability, the combined effect of a number of such mutations should significantly increase a protein s stability. 

Figure 17.5 Diagram of the T4 lysozyme stmcture showing the iocations of two mutations that stabilize the protein stmcture by providing eiectrostatic interactions with the dipoles of a helices. (Adapted from H. Nicholson et al.. Nature 336 651-656, 1988.)...

Alber, T. Mutational effects on protein stability. Annu. Rev. Biochem. 58 765-798, 1989. 

Since we will be dealing with finite graphs, we can analyze the behavior of random Boolean nets in the familiar fashion of looking at their attractor (or cycle) state structure. Specifically, we choose to look at (1) the number of attractor state cycles, (2) the average cyclic state length, (3) the sizes of the basins of attraction, (4) the stability of attractors with respect to minimal perturbations, and (4) the changes in the attractor states and basins of attraction induced by mutations in the lattice structure and/or the set of Boolean rules. 

---