Protein combinatorial space

Finally, the region of accessible protein sequence space was extended by developing a modified version of Stemmer s combinatorial multiple-cassette mutagenesis (CMCM)... 

Even if we restrict our design to a small number of sites in the protein, the combinatorial possibilities quickly approach astronomical dimensions. If we consider mutations at 10 sites and a subset of 10 amino acids, we have 1010 possible variants. Although experimental approaches are under development that can actually search large subsets of protein sequence space, it is not at all a small feat to identify those variants that give rise to a stable structure and at the same time come close to the desired features. Therefore, computational approaches that, with some reliability, are able to pick those variants having a stable structure are desirable instruments in the protein engineer s toolbox. 

Subsequent directed evolution work on Pseudomonas aeruginosa demonstrates that protein sequence space with respect to enantioselectivity is best explored by a three-step procedure (Reetz, 2001) (i) generation of mutants by error-prone PCR at a high-mutation rate (ii) identification of hot regions and spots in the enzyme by error-prone PCR and substantiation by simplified combinatorial multiple-cassette mutagenesis (iii) extension of the process of combinatorial multiple-cassette mutagenesis to cover a defined region of protein sequence space. 

The starting point for further exploration of protein sequence space was the conjecture that Stemmer s method of Combinatorial Multiple Cassette Mutagenesis (CMCM) [74] can be applied in appropriately modified form. It is a special type of DNA-shuffling which can be used to generate mutant gene libraries in which cassettes composed of random or defined sequences and the wild-type are incorporated randomly. CMCM had been developed for use in the area of functional antibodies [74],... 

The space to be searched in protein combinatorial chemistry experiments is extremely large. Consider, for example, that a relatively short lOO-amino acid protein domain were to be evolved. The number of possible amino acid sequences of this length is 20 ° 10 ", since there are 20 naturally occurr-... 

Site-directed mutagenesis has been a valuable method for the engineering of many proteins, but a significant limitation on this technique is that it can be difficult to know what mutations should be made in order to obtain a desired functionality. For example, in order to increase the thermostability of a protein, it is not clear by looking at a 3-D structure which amino acid side chains will affect this trait. In addition, improvements made in the thermostability of the enzyme may adversely affect other properties of the protein, such as enzymatic activity. Therefore, there has been a good deal of interest in combinatorial methods for protein engineering, which can be used to sample a large area of the protein solution space, and thus rapidly identify proteins with desired functionalities. 

The sequence space of proteins is extremely dense. The number of possible protein sequences is 20. It is clear that even by the fastest combinatorial procedure only a very small fraction of such sequences could have been synthesized. Of course, not all of these sequences will encode protein stmctures which for functional purjDoses are constrained to have certain characteristics. A natural question that arises is how do viable protein stmctures emerge from the vast sea of sequence space The two physical features of folded stmctures are (l)in general native proteins are compact but not maximally so. (2) The dense interior of proteins is largely made up of hydrophobic residues and the hydrophilic residues are better accommodated on the surface. These characteristics give the folded stmctures a lower free energy in comparison to all other confonnations. 

Complex optimization of the ligand-protein interactions require to scan large areas of the chemical space. Thus, the combinatorial chemist aims not at the preparation of single compounds but of chemical libraries. Chemical libraries can be produced as collections of single compounds or as defined mixtures. 

Software tools for virtual screening can be best classified by the input data available for screening. On the one side, there is always a collection of compounds to be screened, which differs in size (from a few tens to several millions) and in structure (from structurally unrelated compounds via combinatorial libraries to chemistry spaces). On the other side, there is the data that is used to create the screening query, which can be a protein structure, a known active compound or a pharmacophore created from several known actives (see Figure 4.1). In summary, we are ending up with four classes of screening tools ... 

Virtual screening applications based on superposition or docking usually contain difficult-to-solve optimization problems with a mixed combinatorial and numerical flavor. The combinatorial aspect results from discrete models of conformational flexibility and molecular interactions. The numerical aspect results from describing the relative orientation of two objects, either two superimposed molecules or a ligand with respect to a protein in docking calculations. Problems of this kind are in most cases hard to solve optimally with reasonable compute resources. Sometimes, the combinatorial and the numerical part of such a problem can be separated and independently solved. For example, several virtual screening tools enumerate the conformational space of a molecule in order to address a major combinatorial part of the problem independently (see for example [199]). Alternatively, heuristic search techniques are used to tackle the problem as a whole. Some of them will be covered in this section. 

In nature, the evolution of molecules with desired properties may be regarded as a combinatorial optimisation strategy to find solutions in a search space of unlimited size and diversity. Thus, the number of all possible, different proteins comprising only 200 amino acids is 20200, a number that is much larger than the number of particles in the universe (estimated to be in the range of 1088). Similarly, the number of different... 

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