Search and analysis of the sequence space of a protein using computational tools

The application of enzymes as catalysts for industrial processes spawned what is now a rapidly growing field of biocatalysis. Numerous enzymes have been found and characterized according to their functions and/or three-dimensional structures. Directed Evolution (DE) is a field of research in biocatalysis, where mutations are made in the sequence of a native or what can be called a wild-type enzyme. These mutations are made at random, with the purpose of finding an alternate sequence or a variant to the wild-type enzyme, which shows an improvement over it for a specific property. The sequence space of an enzyme refers to all the possible variants, which can be created from it. Due to an immensely large number of such sequences, making mutations at random is definitely not an optimal strategy. However, due to the absence of a proper understanding of how the sequence of a protein translates into its function, or a sequence-to-function map, DE is usually the only available option. In this thesis, a computational approach to improving the process of DE is presented, which involves using machine learning algorithms. When any enzyme is subjugated to DE, a large number of its variants are created, which are analyzed through high-throughput screening methods. The screening results provide us the measure of the property of interest, like catalytic activity towards a specific reaction, for each of these variants. This data can be utilized to search for patterns in the sequence space, which can lead us to an understanding of how the function is related to an enzyme's sequence. However, the critical limitation to this approach is the scarcity to data because sequencing the created variants is a sizeable task and only a relatively small number can be expected to be available. Most machine learning methods, on the other hand, usually required a large number of examples in the data set. To circumvent this constraint, a simplifying assumption was made, whereby, each variant was divided into two classes---positive and negative. This criteria for this division can be selected based on the measured property of interest for the variant, according to the screening method. Such an assumption reduces the problem to a case of non-linear classification into binary classes. Efficient algorithms have been developed for such problems, which may be able to give pertinent results from the available data. Chapters 1 and 2 of this thesis introduce the basic concepts of protein engineering and Directed Evolution. The suggested approach of using machine learning to analyze the sequence space of any protein or enzyme is described. Chapter 2 also provides background information on the different experimental procedures, which are performed during a DE process. It also mentions the research done in the field of applying different computational strategies to improve DE. Background is provided on the different machine learning algorithms, which were used with the data available from DE. Support Vector Machines (SVMs) are a recently developed class of algorithms, which are primarily used for non-linear classification. An SVM was formulated to identify important amino acids in the sequence of a protein, which is described in Chapter 3. An important amino acid residue was defined as one, which, if mutated, will result in an inactive variant. The data used were the variant sequences containing random mutations created by using different protocols of DE. Based on their screening, they were classified as positive, if they had any catalytic activity, or negative, if they had none. This algorithm was applied to the TEM-1 β-lactamase sequence. The reason for this choice was the availability of known significant amino acid residues for the TEM-1 β-lactamase sequence, which were found through extensive experiments. In silico or computer-generated variants were created by simulating the different protocols of DE. It was shown that the SVM can efficiently identify such residues from relatively small number (of the order of 102) of variant sequences. Chapter 4 extends the framework described in Chapter 3 to identify pairs of amino acids, which interact with each other. Only interactions that contribute significantly to the function or structural stability of the protein need to be identified. Boolean Learning, which is another class of machine learning problems, was used for this purpose. The specific algorithm used was called OCAT (One Clause At a Time). The data assumed in this case were the variant sequence created specifically from the recombinant protocols (described in Chapter 2) of DE. The definition for positive and negative variants were catalytically active or inactive respectively. It was shown through simulations that the OCAT algorithm can identify the interacting pairs in the sequence. This result was also shown to be independent of where the individual amino acids, involved in the interaction, exist in the primary sequence of the protein. A novel way of combining the OCAT algorithm with SVMs was also introduced. It was shown that the results obtained for the combination of these two algorithms, which was referred to as BLSVM, were better than OCAT alone. It was also suggested that the results obtained by using these algorithms on the variants generated in one round of DE can help improve the fraction of active or positive variants in the subsequent rounds. This was done by not permitting any mutations to occur in the amino acids, which interact with each other. To show the applicability of the algorithm described in Chapter 4, an experimental study is presented in Chapter 5. Two fluorescent proteins---mRFP and DsRed---were subjected to different recombinant protocols and 83 unique variants were generated. The positive variants were defined as ones that fluoresce with at least 10% of the intensity of the two parent enzymes. Using the OCAT algorithm on these sequences, a pair of possibly interacting residues was identified. The three-dimensional structure of DsRed showed that these two residues were very close to each other and were also close to the chromophore, which imparts the fluorescence to the two parent enzymes. The interaction between these residues was experimentally confirmed with the help of point mutations. The claim that this result can help increase the fraction active sequences in the variants of subsequent rounds, was also justified by doing further recombinant experiments where the two identified amino acids were not allowed to be mutated. The results showed close to 20% improvement in the fraction positive variants when compared with the recombinant variants of the two parent sequences. On analyzing the variants created in Chapter 5, it was observed that often the screening procedure can give erroneous results. Thus, there is a finite probability of misclassifying a variant, which is known as classification error of classification noise. Unfortunately, the OCAT algorithm, which was used in Chapters 4 and 5 is highly sensitive to classification noise and does not perform well. Thus, an alternate algorithm was presented in Chapter 6, which was derived from OCAT but is tolerant to classification noise. This algorithm, which was termed Modified OCAT or mOCAT, was theoretically analyzed. Using the PAC learning theory for Boolean Learning, it was shown that mOCAT is efficient and can be used for sample sets with classification noise less than 50%. An expression was developed for the number of examples required, which will ensure that the learning is going to be accurate. mOCAT was simulated for the same problem, which was described in Chapter 4. It was shown that in the presence of classification noise, mOCAT can outperform, not only OCAT, but also another existing algorithm. In conclusion, Chapter 7 provides the significant findings and overall achievements of this thesis. The approach of identifying indivi