Nonadditivity of mutational effects on the properties of catalase I and its application to efficient directed evolution

Renewable Energy Driven by Le Chatelier's Principle, Enzyme Function, and Non-Additive Contributions to Ion Fluctuations: A Hypothesis in Biomechanical and Nanotechnology Energy Theory

The search for green energy sources has populated the research arena with significant emphasis on green electronics, green fuels, and green batteries that reduce waste, emissions, and environmental toxicity. Simultaneously, nanotechnology has developed substantially in the recent years and the emerging area of nanoenergetics has shown impressive discoveries that can aid in the search for alternative and green energies. The use of exotic materials in these fields and even enzymes has led scientists to be able to cross-link biomolecules and nanotechnology circuits, which can be important points in the search of novel energy searches. This paper discusses a biochemical energy-generating unit driven by ion fluctuations and spontaneous enzyme conformational changes. The paper lays also the theoretical thermodynamical foundation of the nanoenergy unit and to exploit the principle of nonadditivity and equilibrium as main forces in driving an energy-generating reaction.

Quantifying epistatic interactions among the components constituting the protein translation system

In principle, the accumulation of knowledge regarding the molecular basis of biological systems should allow the development of large-scale kinetic models of their functions. However, the development of such models requires vast numbers of parameters, which are difficult to obtain in practice. Here, we used an in vitro translation system, consisting of 69 defined components, to quantify the epistatic interactions among changes in component concentrations through Bahadur expansion, thereby obtaining a coarse-grained model of protein synthesis activity. Analyses of the data measured using various combinations of component concentrations indicated that the contributions of larger than 2-body inter-component epistatic interactions are negligible, despite the presence of larger than 2-body physical interactions. These findings allowed the prediction of protein synthesis activity at various combinations of component concentrations from a small number of samples, the principle of which is applicable to analysis and optimization of other biological systems. Moreover, the average ratio of 2- to 1-body terms was estimated to be as small as 0.1, implying high adaptability and evolvability of the protein translation system.

New insight into long-range nonadditivity within protein double-mutant cycles

Additivity principles in chemistry, biochemistry, and biophysics have been used extensively for decades. Nevertheless, it is well known that additivity frequently breaks down in complex biomacromolecules. Nonadditivity within protein double mutant free energy cycles of spatially close residue pairs is a generally well-understood phenomenon, whereas a robust description of nonadditivity extending over large distances remains to be developed. Here, we test the hypothesis that the mutational effects tend to be nonadditive if two structurally well-separated mutated residues belong to the same rigid cluster within the wild type protein, and additive if they are located within different clusters. We find the hypothesis to be statistically significant with P-values that range from 10(-5) to 10(-6). To the best of our knowledge, this result represents the first demonstration of a statistically significant preponderance for nonadditivity over long distances. These findings provide new insight into the origins of long-range nonadditivity in double mutant cycles, which complements the conventional wisdom that nonadditivity arises in double mutations involving contacting residues. Consequently, these results should have far-reaching implications for a proper understanding of protein stability, structure/function analyses, and protein design.

Dissecting protein structure and function using directed evolution

To characterize the contributions of individual amino acids to the structure or function of a protein, researchers have adopted directed evolution approaches, which use iterated cycles of mutagenesis and selection or screening to search vast areas of sequence space for sets of mutations that provide insights into the protein of interest.

Experimental rugged fitness landscape in protein sequence space

The fitness landscape in sequence space determines the process of biomolecular evolution. To plot the fitness landscape of protein function, we carried out in vitro molecular evolution beginning with a defective fd phage carrying a random polypeptide of 139 amino acids in place of the g3p minor coat protein D2 domain, which is essential for phage infection. After 20 cycles of random substitution at sites 12–130 of the initial random polypeptide and selection for infectivity, the selected phage showed a 1.7×10⁴-fold increase in infectivity, defined as the number of infected cells per ml of phage suspension. Fitness was defined as the logarithm of infectivity, and we analyzed (1) the dependence of stationary fitness on library size, which increased gradually, and (2) the time course of changes in fitness in transitional phases, based on an original theory regarding the evolutionary dynamics in Kauffman's n-k fitness landscape model. In the landscape model, single mutations at single sites among n sites affect the contribution of k other sites to fitness. Based on the results of these analyses, k was estimated to be 18–24. According to the estimated parameters, the landscape was plotted as a smooth surface up to a relative fitness of 0.4 of the global peak, whereas the landscape had a highly rugged surface with many local peaks above this relative fitness value. Based on the landscapes of these two different surfaces, it appears possible for adaptive walks with only random substitutions to climb with relative ease up to the middle region of the fitness landscape from any primordial or random sequence, whereas an enormous range of sequence diversity is required to climb further up the rugged surface above the middle region.

In vitro evolution of proteins

Consecutive rounds of diversification and selection of the fittest is believed to be the main driving force for the evolution of life. For the evolution of life to proceed, all living cells are surrounded by a lipid bilayer that separates their own genes from the external environment and from those of other organisms. In this way, the genetic information of an individual is replicated on the basis of their phenotype; thus the enrichment of the fittest will occur. Hence, evolution is based on linkage between genotype and phenotype owing to the surrounding of the genetic material with a barrier. The linkage between genotype and phenotype is also known to be essential for the directed evolution of proteins. Indeed, systems for molecular evolution, including phage display, ribosome display, and in vitro compartmentalization, all satisfy this requirement in different ways. These systems have been shown to be powerful tools for high-throughput screening for the functions of proteins, screening as many as <10(12) molecules in 1 d. These selection systems in combination with various gene libraries yield proteins with improved or altered biophysical properties, and may even allow the generation of proteins with novel functions.

On the relation between fluctuation and response in biological systems

A general relationship between fluctuation and response in a biological system is presented. The fluctuation is given by the variance of some quantity, whereas the response is given as the average change of that quantity for a given parameter change. We propose a relationship where the two are proportional, in a similar way to the fluctuation-dissipation theorem in physics. By studying an evolution experiment where fluorescence of protein in bacteria increases, we confirm our relation by observing a positive correlation between the speed of fluorescence evolution and the phenotypic fluctuation of the fluorescence over clone bacteria. The generality of the relationship as well as its relevance to evolution is discussed.

Developments and trends in enzyme catalysis in nonconventional media

The conventional notion that enzymes are only active in aqueous media has long been discarded, thanks to the numerous studies documenting enzyme activities in nonaqueous media, including pure organic solvents and supercritical fluids. Enzymatic reactions in nonaqueous solvents offer new possibilities for producing useful chemicals (emulsifiers, surfactants, wax esters, chiral drug molecules, biopolymers, peptides and proteins, modified fats and oils, structured lipids and flavor esters). The use of enzymes in both macro- and microaqueous systems has been investigated especially intensively in the last two decades. Although enzymes exhibit considerable activity in nonaqueous media, the activity is low compared to that in water. This observation has led to numerous studies to modify enzymes for specific purposes by various means including protein engineering. This review covers the historical developments, major technological advances and recent trends of enzyme catalysis in nonconventional media. A brief description of different classes of enzymes and their use in industry is provided with representative examples. Recent trends including use of novel solvent systems, role of water activity, stability issues, medium and biocatalyst engineering aspects have been discussed with examples. Special attention is given to protein engineering and directed evolution.

Molecular evolution in static and dynamical landscapes

In an attempt to understand protein evolution, we address the issues ofhow much variety in the sequences is needed to prompt the evolution ofan enzyme from random polypeptides and how does cellular interactionaffect the dynamics of molecular evolution to allow genetic diversity inpopulation. The experimental evolution of phage-displayed randompolypeptides of about 140 amino acid residues panned with transition stateanalogue for an esterase reaction showed that even with a population sizeas small as ten, not only could significant varieties be found but also therandom polypeptides in each of the generation had great promise towardsdeveloping into functional proteins. Hence, it is evident that the enzymeevolution is prompted even within a small local area of the static landscapeof the sequence space. Considering that interaction among living cells is aninevitable event in natural evolution, its role was investigated through threeconsecutive rounds of random mutagenesis on the glutamine synthetasegene and chemostat culture of the transformed Escherichia colicellscontaining the mutated genes. The molecular phylogeny and populationdynamics show the coexistence of some mutants having different level ofglutamine synthetase at each generation. In addition, it was confirmed thatcellular interaction via the medium influences the stability of the coexistenceand bring forth fitness change to the coexisting members of the population,thereby, leading to a dynamical landscape. Based on experimental resultsreflecting the extent of interaction among members in population, here, Iproposed that protein evolution could change its mode from theoptimization on static landscape to diversification on dynamicallandscape.

Correlation between the conformation space and the sequence space of Peptide chain

Effects of point mutations are investigated in a computer model ofsequence selection. In the model, sequences are selected according totheir functional ability defined by the configuration at the active site.Through such functional selection on the local configuration, sequenceswhich fold globally into a unique conformation can be selected from randomsequences. The selected sequence accepts many point mutations as neutralmutations. More structurally fluctuating sites in the chain accept alarger variety of point mutations, which shows correlation between theconformational fluctuation and the sequence fluctuation.

Evolvability of random polypeptides through functional selection within a small library

A directed evolution with phage-displayed random polypeptides of about 140 amino acid residues was followed until the sixth generation under a selection based on affinity to a transition state analog for an esterase reaction. The experimental design deliberately limits the observation to only 10 clones per generation. The first generation consists of three soluble random polypeptides and seven arbitrarily chosen clones from a previously constructed library. The clone showing the highest affinity in a generation was selected and subjected to random mutagenesis to generate variants for the next generation. Even within only 10 arbitrarily chosen polypeptides in each of the generations, there are enough variants in accord to capacity of binding affinity. In addition, the binding capacity of the selected polypeptides showed a gradual continuous increase over the generation. Furthermore, the purified selected random polypeptides exhibited a gradual but significant increase in esterase activity. The ease of the functional development within a small sequence variety implies that enzyme evolution is prompted even within a small population of random polypeptides.

Importance of compartment formation for a self-encoding system

A self-encoding system designed to have strict "compartition" of the molecules, i.e., to contain only a single molecule of DNA in each compartment, was established, and its evolutionary fate was analyzed. The system comprised the Thermus thermophilus DNA polymerase gene as the informational molecule and its protein product replicating the gene as the functional molecule. Imposing strict compartition allows the self-encoding system to last up to at least the tenth generation, whereas the system ceased to work after the third generation when loose compartition initiated with 100 molecules was imposed. These results provide experimental evidence on the importance of compartition for the maintenance of a self-encoding system. In addition, the extent of diversity in self-replication activity of the compartments was found to be another vital difference in the evolutionary dynamics between the strict and loose compartitions. Although the system with strict compartition provides widely diversified activity of the compartments at each generation, the values of the activity diverge only within a small range in the system with loose compartition. When the variety in the activity of a compartment is small, functional selection becomes weak, and to conform Darwinian evolution may become unfeasible. Therefore, strict compartition is essential for the evolvability of a self-encoding system.

Computationally focusing the directed evolution of proteins

Directed evolution has proven to be a successful strategy for the modification of enzyme properties. To date, the preferred experimental procedure has been to apply mutations or crossovers randomly throughout the gene. With the emergence of powerful computational methods, it has become possible to develop focused combinatorial searches, guided by computer algorithms. Here, we describe several computational methods that have emerged to aid the optimization of mutant libraries, the targeting of specific residues for mutagenesis, and the design of recombination experiments.

De novo design of biocatalysts

The challenging field of de novo enzyme design is beginning to produce exciting results. The application of powerful computational methods to functional protein design has recently succeeded at engineering target activities. In addition, efforts in directed evolution continue to expand the transformations that can be accomplished by existing enzymes. The engineering of completely novel catalytic activity requires traversing inactive sequence space in a fitness landscape, a feat that is better suited to computational design. Optimizing activity, which can include subtle alterations in backbone conformation and protein motion, is better suited to directed evolution, which is highly effective at scaling fitness landscapes towards maxima. Improved rational design efforts coupled with directed evolution should dramatically improve the scope of de novo enzyme design.

Conversion of a typical catalase from Bacillus sp. TE124 to a catalase-peroxidase by directed evolution

We have converted a typical catalase from Bacillus sp. TE124 to a catalase-peroxidase using DNA shuffling and error-prone PCR. A triple mutant, R47H/R356C/D374N, that showed significantly reduced catalase activity and increased peroxidase activity was identified by screening mutant libraries. When single mutant--R47H, R356C and D374N--were generated by site-directed mutagenesis, conserved Arg-47, located on the distal side of the prosthetic heme group in the superfamily of typical catalases, was found to be responsible for the conversion of catalase to catalase-peroxidase. To further clarify the role of Arg-47, arginine was replaced with different amino acids--alanine, lysine, aspartic acid, glutamic acid, glutamine, phenylalanine, tryptophan and tyrosine--and the mutant enzymes were assayed. All of the arginine mutants had increased peroxidase activity coupled with reduced catalase activity. Among these mutants, R47W exhibited the highest peroxidase activity, while R47E and R47Q not only had increased peroxidase activity but also retained relatively high catalase activity. These results suggest that tryptophan plays a key role in the catalytic mechanism of the peroxidase reaction and that glutamic acid and glutamine facilitate both catalatic and peroxidatic reactions.

A cross-section of the fitness landscape of dihydrofolate reductase

In vitro molecular evolution is regarded as a hill-climbing on a fitness landscape in sequence space, where the 'fitness' is a quantitative measure of a certain physicochemical property of a biopolymer. We analyzed a 'cross-section' of the enzymatic activity landscape of dihydrofolate reductase (DHFR) by using a method of analysis of a fitness landscape. We limited the sequence space of interest to the five-dimensional sequence space, where the coordinate corresponds to the 1st, 16th, 20th, 42nd and 92nd site in the DHFR sequence. Thirty six mutants mapped into the limited sequence space were taken in the analysis. As a result, the cross-section is of the rough Mt Fuji type based on the mutational additivity. The ratio of the mean slope to the roughness is 2.8 and the Z-score of the original ratio against a distribution of random references is 7.0, which indicates a large statistical significance. The existence of such a cross-section was discussed in terms of the occurrence probability of sets of five sites distantly separated from each other on the DHFR 3D structure. Our results support the effectiveness of the evolution strategy which exploits the accumulation of advantageous single point mutations in such a cross-section.

Improving the quality of industrially important enzymes by directed evolution

Directed evolution is a new process for developing industrially viable biocatalysts. This technique does not require a comprehensive knowledge of the relationships between sequence structure and function of proteins as required by protein engineering. It mimics the process of Darwinian evolution in a test tube combining random mutagenesis and recombination with screening or selection for enzyme variants that have the desired properties. Directed evolution helps in enhancing the enzyme performance both in natural and synthetic environments. This article reviews the process of directed evolution and its application to improve substrate specificity, activity, enantioselectivity and thermal stability.

Computational method to reduce the search space for directed protein evolution

We introduce a computational method to optimize the in vitro evolution of proteins. Simulating evolution with a simple model that statistically describes the fitness landscape, we find that beneficial mutations tend to occur at amino acid positions that are tolerant to substitutions, in the limit of small libraries and low mutation rates. We transform this observation into a design strategy by applying mean-field theory to a structure-based computational model to calculate each residue's structural tolerance. Thermostabilizing and activity-increasing mutations accumulated during the experimental directed evolution of subtilisin E and T4 lysozyme are strongly directed to sites identified by using this computational approach. This method can be used to predict positions where mutations are likely to lead to improvement of specific protein properties.

Rational evolutionary design: the theory of in vitro protein evolution

Directed evolution uses a combination of powerful search techniques to generate proteins with improved properties. Part of the success is due to the stochastic element of random mutagenesis; improvements can be made without a detailed description of the complex interactions that constitute function or stability. However, optimization is not a conglomeration of random processes. Rather, it requires both knowledge of the system that is being optimized and a logical series of techniques that best explores the pathways of evolution (Eigen et al., 1988). The weighing of parameters associated with mutation, recombination, and screening to achieve the maximum fitness improvement is the beginning of rational evolutionary design. The optimal mutation rate is strongly influenced by the finite number of mutants that can be screened. A smooth fitness landscape implies that many mutations can be accumulated without disrupting the fitness. This has the effect of lowering the required library size to sample a higher mutation rate. As the sequence ascends the fitness landscape, the optimal mutation rate decreases as the probability of discovering improved mutations also decreases. Highly coupled regions require that many mutations be simultaneously made to generate a positive mutant. Therefore, positive mutations are discovered at uncoupled positions as the fitness of the parent increases. The benefit of recombination is twofold: it combines good mutations and searches more sequence space in a meaningful way. Recombination is most beneficial when the number of mutants that can be screened is limited and the landscape is of an intermediate ruggedness. The structure of schema in proteins leads to the conclusion that many cut points are required. The number of parents and their sequence identity are determined by the balance between exploration and exploitation. Many disparate parents can explore more space, but at the risk of losing information. The required screening effort is related to the number of uphill paths, which decreases more rapidly for rugged landscapes. Noise in the fitness measurements causes a dramatic increase in the required mutant library size, thus implying a smaller optimal mutation rate. Because of strict limitations on the number of mutants that can be screened, there is motivation to optimize the content of the mutant library. By restricting mutations to regions of the gene that are expected to show improvement, a greater return can be made with the same number of mutants. Initial studies with subtilisin E have shown that structurally tolerant positions tend to be where positive activity mutants are made during directed evolution. Mutant fitness information is produced by the screening step that has the potential to provide insight into the structure of the fitness landscape, thus aiding the setting of experimental parameters. By analyzing the mutant fitness distribution and targeting specific regions of the sequence, in vitro evolution can be accelerated. However, when expediting the search, there is a trade-off between rapid improvement and the quality of the long-term solution. The benefit of neutrality has yet to be captured with in vitro protein evolution. Neutral theory predicts the punctuated emergence of novel structure and function, however, with current methods, the required time scale is not feasible. Utilizing neutral evolution to accelerate the discovery of new functional and structural solutions requires a theory that predicts the behavior of mutational pathways between networks. Because the transition from neutral to adaptive evolution requires a multi-mutational switch, increasing the mutation rate decreases the time required for a punctuated change to occur. By limiting the search to the less coupled region of the sequence (smooth portion of the fitness landscape), the required larger mutation rate can be tolerated. Advances in directed evolution will be achieved when the driving forces behind such proce

Structure-based chimeric enzymes as an alternative to directed enzyme evolution: phytase as a test case

Thermostability is a key feature for commercially attractive variants of the fungal enzyme phytase. In an initial set of experiments, we restored ionic interactions and hydrogen bonds on the surface of Aspergillus terreus phytase, which are present in the homologous but more thermostable enzyme from A. niger. Since these mutations turned out to be neutral, we replaced-in the same region and based on the crystal structure of A. niger phytase-entire secondary structure elements. The replacement of one alpha-helix on the surface of A. terreus phytase by the corresponding stretch of A. niger phytase resulted in an enzyme with improved thermostability and unaltered enzymatic activity. Surprisingly, the thermostability of this hybrid protein was very similar to that of A. niger phytase, although the fusion protein contained only a 31 amino acid stretch of the more stable parent enzyme. This report provides evidence that structure-based chimeric enzymes can be used to exploit the evolutionary information within a sequence alignment. We propose this method as an alternative to directed enzyme evolution if due to expression constraints the screening of large mutant populations is not feasible.

Theory of evolutionary molecular engineering through simultaneous accumulation of advantageous mutations

We examined the effectiveness of an "adaptive leap" strategy using the "mutation scrambling" method as an efficient optimization technique (Uchiyama, 2000;J. Biochem.128, 441-447) for cases where mutational (rough) additivity holds in fitness. The mutation scrambling method is composed of the following three processes: (1) preliminary selection of several advantageous single-point mutations introduced in a wild-type sequence; (2) preparation of various multiple-point mutants incorporating the advantageous mutant residue or wild-type residue at each of the selected sites, by scrambling the mutant residues and wild-type residues (this process is called mutation scrambling); and (3) selection of the fittest through screening of the mutant pool. The fitness distribution in the mutant pool is controlled by the mixing ratio of the mutant residues to the wild-type residues. We focused on the mutant fitness distribution and obtained the optimal mixing ratio which efficiently generates superior multiple-point mutants with high fitnesses. As a result, we found that the optimal ratio lies between 7/3 and 9/1 in realistic cases. Particularly, this strategy works well in cases where the number of component mutations is large and the size of the population to be screened is small. Analysis of the mutant fitness distributions with various mixing ratios is also useful to explore local fitness landscapes.

Directed evolution of toluene dioxygenase from Pseudomonas putida for improved selectivity toward cis-indandiol during indene bioconversion

Toluene dioxygenase (TDO) from Pseudomonas putida F1 converts indene to a mixture of cis-indandiol (racemic), 1-indenol, and 1-indanone. The desired product, cis-(1S,2R)-indandiol, is a potential key intermediate in the chemical synthesis of indinavir sulfate (Crixivan), Merck's HIV-1 protease inhibitor for the treatment of AIDS. To reduce the undesirable byproducts 1-indenol and 1-indanone formed during indene bioconversion, the recombinant TDO expressed in Escherichia coli was evolved by directed evolution using the error-prone polymerase chain reaction (epPCR) method. High-throughput fluorometric and spectrophotometric assays were developed for rapid screening of the mutant libraries in a 96-well format. Mutants with reduced 1-indenol by-product formation were identified, and the individual indene bioconversion product profiles of the selected mutants were confirmed by HPLC. Changes in the amino acid sequence of the mutant enzymes were identified by analyzing the nucleotide sequence of the genes. A mutant with the most desirable product profile from each library, defined as the most reduced 1-indenol concentration and with the highest cis-(1S,2R)-indandiol enantiomeric excess, was used to perform each subsequent round of mutagenesis. After three rounds of mutagenesis and screening, mutant 1C4-3G was identified to have a threefold reduction in 1-indenol formation over the wild type (20% vs 60% of total products) and a 40% increase of product (cis-indandiol) yield.

Analysis of a local fitness landscape with a model of the rough Mt. Fuji-type landscape: application to prolyl endopeptidase and thermolysin

A method of analysis of a local fitness landscape for a current biopolymer is presented. Based on the assumption of additivity of mutational effects in the biopolymer, we assigned a site-fitness to each residue at each site. The assigned values of site-fitnesses were obtained by the least-squares method to minimize discrepancies between experimental fitnesses and theoretical ones. As test cases, we analyzed a section of a local landscape for the thermostability of prolyl endopeptidase and that for the enzymatic activity of thermolysin. These sections were proved to be of the rough Mt. Fuji-type with straight theta values of larger than 1.0, where straight theta is defined as the ratio of the "mean slope" to the "degree of roughness" on the fitness surface. Furthermore, we theoretically explained discrepancies between the fitnesses of multiple mutants and those predicted based on strict additivity of the component mutations by using a model of the rough Mt. Fuji-type landscape. According to this model, the discrepancies depend on the local landscape property (such as the straight theta value) and the location of the wild type on the landscape and the mean change in fitness by the component mutations. Our results suggest that this model may provide a good approximation of real sections of local landscapes for current biopolymers phenomenologically.

Directed evolution of microbial oxidative enzymes

In the past year, a number of oxidative enzymes have been the target of directed evolution. Catalase reaction specificity has been shifted to peroxidase, the high pH, thermal and oxidative stability of a fungal peroxidase has been dramatically improved, and the substrate specificity of cytochrome P450 has been altered to include substrates that the wild-type enzymes are incapable of oxidizing.

Construction and characterization of phage libraries displaying artificial proteins with random sequences

Three phage libraries, PL1, PL2, and PL3, displaying artificial proteins with random sequences were constructed. The artificial proteins, which are model of ancestral proteins, are derivatives of the 25 kinds of random proteins with about 140 amino acid residues produced via random mutagenesis and combinatorial recombination. The random proteins were displayed on the surface of filamentous bacteriophage as fusion protein with the pIII coat protein at an estimated average number on the phage particles in PL1, PL2, and PL3 of 0.32, 0.32, and 0.08, respectively. Each library was shown to express 10(5) to 10(6) kinds of random proteins. With the phage libraries displaying long random peptides, we now have an effective selection system to observe in vitro evolution of new functional proteins from artificial proteins with random sequences.

Evolutionary molecular engineering by random elongation mutagenesis

We describe a new method of random mutagenesis that employs the addition of peptide tails with random sequences to the C-terminal of enzyme molecules. A mutant population of catalase I from Bacillus stearothermophilus prepared by this method has a diversity in thermostability and enzyme activity equal to that obtained after random point mutagenesis. When a triple mutant of catalase I (I108T/D130N/1222T)-the thermostability of which is much lower than that of the wild type-was subjected to random elongation mutagenesis, we generated a mutant population containing only mutants with higher thermostability than the triple mutant. Some had an even higher stability than the wild-type enzyme, whose thermostability is considered to be optimized. These results indicate that peptide addition expands the protein sequence space resulting in a new fitness landscape. The enzyme can then move along the routes of the new landscape until it reaches a new optimum. The combination of random elongation mutagenesis with random point mutagenesis should be a useful approach to the in vitro evolution of proteins with new properties.