Several lines of evidence suggest that flexible regions within a protein are its weakest spots. These regions unfold first and mutations in these regions often stabilize proteins. Enzymes from mesophiles are on average more flexible that those from thermophiles and they are also less stable. Flexibility regions of a protein may also promote aggregation. Partial unfolding can expose hydrophobic groups, which can then aggregate with other partly unfolded proteins.
Flexibility itself is not destabilizing; in contrast, flexibility is a stabilizing feature because it increases entropy. However, flexibility regions in a folded protein shows that interactions with other amino acids are weak in that region. Flexibility shows where one could create stronger interactions. The stronger interactions will decrease flexibility, which will reduce the stability, but this loss is expected to be small (perhaps a factor of two, or 0.4 kcal/mol). The gain in stability created by new interactions between amino acids such as hydrogen bonds and hydrophobic interactions (several kcal/mol) should more than make up for this reduction.
Stabilizing the flexible regions requires new interactions between amino acid residues within and outside this region. Pikkemaat and coworkers (2002) first suggested stabilizing proteins by targeting mutagenesis to flexible regions of proteins. They used molecular dynamics to identify flexible regions, but Reetz and coworkers (2006) later suggested a simpler method: to target the residues with the highest B-factors in their crystal structures (B-fit method). This approach works sometimes, but fails in other cases (Kim et al., 2010). Floor and coworkers (2014) suggested a more nuanced approach. While they agree that the goal is to stabilize flexible regions, they found that substitutions next to flexible regions can be more effective than substitutions within the flexible regions. Thus, stabilizing a flexible regions may require changes within the flexible region, adjacent to this region or in both regions to create interaction partners.
Flexible regions are typically loops on the surface and at the N- and C-termini of the protein. Mutagenesis in these regions is not likely to disrupt catalytic activity. In some cases, regions of the active site are flexible. Increasing interactions between amino acids within an active site can also stabilize a protein (Floor et al., 2014; Xie et al., 2014), but this approach risks damaging the catalytic activity.

Note: One can also stabilize proteins by reducing the flexibility of the unfolded form. In this case, substitutions do not change interactions between amino acids in the folded or unfolded form. The goal is only to reduce the flexibility of the unfolded form and thus to reduce the entropy that favors unfolding. For example, replacing glycine residues with alanine in a spot that does not affect the folded form will reduce the number of conformations available to the unfolded form by a factor of 3.3. The reduced flexibility corresponds to an entropy contribution of ~0.7 kcal/mol at 300 °K (Matthews et al., 1987). The unfolded form will be slightly less flexible and therefore slightly less stable, thus shifting the folded-unfolded equilibrium toward the folded form. In contrast, the goal of stabilizing flexible regions of the folded form is to increase the interactions between the amino acids. Reducing entropy of the folded is a penalty that must be overcome by the stronger interactions to get a net stabilization of the folded form.

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R. J. Floor, H. J. Wijma, D. I. Colpa, A. Ramos-Silva, P. A. Jekel, W. Szymanski, B. L. Feringa, S. J. Marrink, D. B. Janssen (2014) Computational library design for increasing haloalkane dehalogenase stability. ChemBioChem 15, 1660-72.
H. S. Kim, Q. A. T. Le, Y. H. Kim (2010) Development of thermostable lipase B from Candida antarctica (CalB) through in silico design employing B-factor and RosettaDesign. Enzyme Microb Tech 47, 1-5.
B. W. Matthews, H. Nicholson, J. W. Becktel (1987) Enhanced protein thermostability from site-directed mutations that decrease the entropy of unfolding. Proc Natl Acad Sci USA, 84, 6663-7.
M. G. Pikkemaat, A. B. M. Linssen, H. J. C. Berendsen, D. B. Janssen (2002), Molecular dynamics simulations as a tool for improving protein stability, Prot. Eng., 15, 185-92.
M. T. Reetz, J. D. Carballeira, A. Vogel (2006) Iterative saturation mutagenesis on the basis of B factors as a strategy for increasing protein thermostability. Angew. Chem. Int. Ed. Engl. 45, 7745-51.
Y. Xie, J. An, G. Yang, G. Wu, Y. Zhang, Cui, L., Y. Feng (2014) Enhanced enzyme kinetic stability by increasing rigidity within the active site. J Biol Chem 289, 7994-8006.

Instead of the NNK codon for saturation mutagenesis, one can use the NNS codon. Is one a better choice? Maybe. K represents G or T, while S represents G or C. The sixteen codons that contain G in the last position are identical in both choices of degenerate codon. The remaining sixteen codons are NNT for NNK degenerate codon, but are NNC for NNS degenerate codon. These sixteen codons are synonymous, so they encode the same amino acids. They do differ at the level of nucleotides - the NNS-containing primer has a higher GC content. While the NNK degenerate primer contains five rare codons, it includes synonymous non-rare codons. In contrast, the NNS degenerate primer lacks a synonymous non-rare codon for arginine, so variants with this amino acid substitution may express poorly. (This potential problem only occurs in yeast; no problems predicted for expression in E. coli.) The melting temperature of the NNS degenerate primer will be slightly higher than the NNK degenerate primer, which, depending on the partner primer, may be an advantage. Choosing between NNK and NNS may also minimize formation of primer hairpins or primer dimers.

The current cycle of carbon atoms in fuels is too slow to be sustainable. Fuels and chemicals come from petroleum. Fuels are burned releasing the carbon as carbon dioxide. Plastics are used, then landfilled. To reuse these carbon atoms, the carbon dioxide and landfill contents must be converted back to plants, but currently this is too slow. Too much carbon dioxide is released and the conversion of landfill to plant nutrients is too slow. The cycle is not turning. Even if these problems could be solved, an even bigger one remains. Converting plants to petroleum takes eons.
broken carbon cycle.png
The broken carbon cycle.

One solution is new biocatalysis reactions. One set is biofuels and biorefinery processes to convert plants directly to fuels and chemicals. The second set is biodegradation of plastics and other chemicals to plant nutrients. Inventing these reactions using synthetic biology and protein engineering is an important goal of biocatalysis today.
sustainable carbon cycle.png
A sustainable carbon cycle needs new biocatalysis processes.

The extent of changes made in the course of a protein improvement has increased dramatically in the past decade. In the early 2000's one or two mutations were typical, while by 2010, 30-40 amino acid substitutions are not unusual. For example, directed evolution of halohydrin dehalogenase for manufacture of the atorvastatin (Lipitor) side chain changed at least 35 of the 254 amino acids (>14%; Fox et al. 2007) and directed evolution of the transaminase for sitagliptin manufacture changed 27 of the 330 amino acids (8.2%; Savile et al. 2010). Similarly, computational design of a retro aldolase required 8 or 12 amino acid substitutions (4-6%) in the starting enzyme, a 197-aa xylanase (Jiang et al., 2008).
Amino acid sequences of proteins in mice and human typically differ by 13% (Waterston et al., 2002), so this laboratory evolution of enzymes is equivalent to compressing the 75 million-year-evolution from an early mammal to today's mice and humans into several months of laboratory work. 

Fox, R. J. et al. (2007), Improving catalytic function by ProSAR-driven enzyme evolution, Nature Biotechnol., 25, 338-344.

Jiang, L. et al. (2008), De novo computational design of retro-aldol enzymes, Science, 319, 1387-1391.

Savile, C. K. et al. (2010), Biocatalytic asymmetric synthesis of chiral amines from ketones applied to sitagliptin manufacture, Science, 329, 305-309.

Waterston, R. H. et al. (2002) Initial sequencing and comparative analysis of the mouse genome. Nature, 420, 520-62.