A mechanistic view of enzyme evolution

New enzyme functions often evolve through the recruitment and optimization of latent promiscuous activities. How do mutations alter the molecular architecture of enzymes to enhance their activities? Can we infer general mechanisms that are common to most enzymes, or does each enzyme require a unique optimization process? The ability to predict the location and type of mutations necessary to enhance an enzyme's activity is critical to protein engineering and rational design. In this review, via the detailed examination of recent studies that have shed new light on the molecular changes underlying the optimization of enzyme function, we provide a mechanistic perspective of enzyme evolution. We first present a global survey of the prevalence of activity‐enhancing mutations and their distribution within protein structures. We then delve into the molecular solutions that mediate functional optimization, specifically highlighting several common mechanisms that have been observed across multiple examples. As distinct protein sequences encounter different evolutionary bottlenecks, different mechanisms are likely to emerge along evolutionary trajectories toward improved function. Identifying the specific mechanism(s) that need to be improved upon, and tailoring our engineering efforts to each sequence, may considerably improve our chances to succeed in generating highly efficient catalysts in the future.     

Accuracy of proofreading with zero energy cost

Accuracy of biological discrimination at the molecular level is known in some systems to involve kinetic proofreading mechanisms. Hopfield and Ninio were the first to propose simple specific kinetic mechanisms for such proofreading and to demonstrate that an energy cost accompanies their improvement in accuracy. Savageau and Freter subsequently derived the explicit cost-accuracy relationship for a broad class of proofreading mechanisms, including the conventional Hopfield-Ninio mechanism just referred to. In other systems, the presence of proofreading mechanisms is in question because the diagnostic features of conventional kinetic proofreading are absent. However, Hopfield has recently proposed an alternative “energy-relay” mechanism, which lacks the characteristic features of conventional proofreading and yet is capable of improving accuracy. In this paper, I use the general cost-accuracy relationship that we have previously derived to examine the energy cost and accuracy of proofreading mechanisms involving an energy relay. The principal findings are the following. First, such mechanisms improve accuracy with a zero cost of proofreading, when “proofreading cost,” defined as the cost due specifically to proofreading, is separated from the costs of putting material through the system. Second, the basic energy-relay mechanism discussed by Hopfield has only a modest improvement in accuracy, but a comparable improvement by a conventional proofreading mechanism would have a cost of about 0·0352 (moles ATP per mole of total product output). Third, accuracy can be increased somewhat if multiple stages of conventional kinetic proofreading precede the energy-relay mechanism. The cost for this improvement is zero while a comparable increase in accuracy achieved by conventional proofreading alone has a cost of about 0·0385. Finally, I propose an alternative arrangement of energy-relay mechanisms that is capable of increasing accuracy still further. The maximum accuracy achieved by this scheme at zero energy cost is comparable to that achieved by an infinite expenditure of energy in a single stage of conventional proofreading.     

Proofreading systems of multiple stages for improved accuracy of biological discrimination

The phenomenal accuracy of biological discrimination is due in many cases to specific proofreading mechanisms. We have previously developed a macroscopic theory of such mechanisms and applied it to the case of single-stage proofreading. In this article we apply the theory to systems with multiple stages of proofreading. A specific relationship between improved accuracy due to proofreading and the associated energy cost is given. This is a macroscopic relationship that must be satisfied regardless of the details of the underlying mechanisms. Five factors in the design of such systems are shown to influence their overall accuracy: (1) initial discrimination, (2) number of proofreading stages, (3) proofreading discrimination of each stage, (4) distribution of proofreading effort among the stages, and (5) total energy expended for proofreading. We show that there is an optimal distribution of proofreading effort that, for a given degree of accuracy, minimizes the energy cost of proofreading. We also provide a simple physical interpretation of this minimum condition. These results are used to examine proofreading in two experimental systems for which there is appropriate data available in the literature: the valyl-tRNA synthetase catalyzed misacylation of tRNA^Val with threonine and the isoleucyl-tRNA synthetase catalyzed misacylation of tRNA^Ile with valine. The correlation between the magnitude of a discrimination factor and the size of the corresponding enzymatic cavity is discussed.     

Multicriteria optimization of biochemical systems by linear programming: application to production of ethanol by Saccharomyces cerevisiae

In this study we present a method for simultaneous optimization of several metabolic responses of biochemical pathways. The method, based on the use of the power law formalism to obtain a linear system in logarithmic coordinates, is applied to ethanol production by Saccharomyces cerevisiae. Starting from an experimentally based kinetic model, we translated it to its power law equivalent. With this new model representation, we then applied the multiobjective optimization method. Our intent was to maximize ethanol production and minimize each of the internal metabolite concentrations. To ensure cell viability, all optimizations were carried out under imposed constraints. The different solutions obtained, which correspond to alternative patterns of enzyme overexpression, were implemented in the original model. We discovered few discrepancies between the S-system-optimized steady state and the corresponding optimized state in the original kinetic model, thus demonstrating the suitability of the S-system representation as the basis for the optimization procedure. In all optimized solutions, the ATP level reached its maximum and any increase in its activity positively affected the optimization process. This work illustrates that in any optimization study no single criteria is of general application being the multiobjective and constrained task the proper way to address it. It is concluded that the proposed multiobjective method can serve to carry out, in a single study, the general pattern of behavior of a given metabolic system with regard to its control and optimization.     

Energy cost of proofreading to increase fidelity of transfer ribonucleic acid aminoacylation.

The paradox of relatively error free function in biological systems composed of relatively error prone components has recently come under intensive investigation. In the case of tRNA aminoacylation, aminoacyl-tRNA synthetases were discovered to have a separate function that allows misacylated molecules to be hydrolyzed more rapidly than correctly acylated molecules. This additional function of the synthetases provides a proofreading or verification mechanism that is believed to improve significantly the overall accuracy of tRNA aminoacylation. In this paper we provide an explicit relationship between the accuracy achieved by proofreading and the energy cost. Experimental data available in the literature are examined in light of this relationship. The following are the principal conclusions from our study: (1) high-accuracy proofreading of tRNA aminoacylation has a high energy cost, as much as 100 times greater than indications from early experimental work; (2) the minimum net error derived in previous theoretical studies is never actually reached; (3) mechanisms in which misacylation and subsequent proofreading occur on the surface of the same synthetase molecule achieve a much higher accuracy than mechanisms in which these functions occur on the surface of different synthetase molecules.     

Kinetic Proofreading at Single Molecular Level: Aminoacylation of tRNAIle and the Role of Water as an Editor

Proofreading/editing in protein synthesis is essential for accurate translation of information from the genetic code. In this article we present a theoretical investigation of efficiency of a kinetic proofreading mechanism that employs hydrolysis of the wrong substrate as the discriminatory step in enzyme catalytic reactions. We consider aminoacylation of tRNA^Ile which is a crucial step in protein synthesis and for which experimental results are now available. We present an augmented kinetic scheme and then employ methods of stochastic simulation algorithm to obtain time dependent concentrations of different substances involved in the reaction and their rates of formation. We obtain the rates of product formation and ATP hydrolysis for both correct and wrong substrates (isoleucine and valine in our case, respectively), in single molecular enzyme as well as ensemble enzyme kinetics. The present theoretical scheme correctly reproduces (i) the amplitude of the discrimination factor in the overall rates between isoleucine and valine which is obtained as (1.8×10²).(4.33×10²) = 7.8×10⁴, (ii) the rates of ATP hydrolysis for both Ile and Val at different substrate concentrations in the aminoacylation of tRNA^Ile. The present study shows a non-michaelis type dependence of rate of reaction on tRNA^Ile concentration in case of valine. The overall editing in steady state is found to be independent of amino acid concentration. Interestingly, the computed ATP hydrolysis rate for valine at high substrate concentration is same as the rate of formation of Ile-tRNA^Ile whereas at intermediate substrate concentration the ATP hydrolysis rate is relatively low. We find that the presence of additional editing domain in class I editing enzyme makes the kinetic proofreading more efficient through enhanced hydrolysis of wrong product at the editing CP1 domain.     

Elucidation of T cell signalling models

A potential mechanism that allows T cells to reliably discriminate pMHC ligands involves an interplay between kinetic proofreading, negative feedback and a destruction of this negative feedback. We analyse a detailed model of these mechanisms which involves the TCR, SHP1 and ERK. We discover that the behaviour of pSHP1 negative feedback is of primary importance, and particularly the influence of a kinetic proofreading base negative feedback state on pSHP1 dynamics. The CD8 co-receptor is shown to benefit from a kinetic proofreading locking mechanism and is able to overcome pSHP1 negative influences to sensitise a T cell.     

Separation of bisdioxopiperazine- and vanadate resistance in topoisomerase II

Bisdioxopiperazines are inhibitors of topoisomerase II trapping this protein as a closed clamp on DNA with concomitant inhibition of its ATPase activity. Here, we analyse the effects of N-terminal mutations identified in bisdioxopiperazine-resistant cells on ATP hydrolysis by this enzyme. We present data consistent with bisdioxopiperazine resistance arising by two different mechanisms; one involving reduced stability of the N-terminal clamp (the N-gate) and one involving reduced affinity for bisdioxopiperazines. Vanadate is a general inhibitor of type P ATPases and has recently been demonstrated to lock topoisomerase II as a salt-stable closed clamp on DNA analogous to the bisdioxopiperazines. We show that a R162K mutation in human topoisomerase II alpha renders this enzyme highly resistant towards vanadate while having little effect on bisdioxopiperazine sensitivity. The implications of these findings for the mechanism of action of bisdioxopiperazines versus vanadate with topoisomerase II are discussed.     

Kinetic analysis of enzyme reactions with slow-binding inhibition.

In this paper we present a general kinetic study of slow-binding inhibition processes, i.e. enzyme reactions that do not respond instantly to the presence of a competitive inhibitor. The analysis that we present is based on the equation that describes the formation of products with time in each case on the experimental progress curve. It is carried out under the condition of limiting enzyme concentration and allows the discrimination between the different cases of slow-binding inhibition. The mechanism in which the formation of complex enzyme-inhibitor is a single or two slow steps or follow a rapid equilibrium, has been considered. The corresponding explicit equations of each case have been obtained and checked by numerical integration. A kinetic data analysis to evaluate the corresponding kinetic parameters is suggested. We illustrate the method, numerically by computer simulation, of the reaction and present some numerical examples that demonstrate the applicability of our procedure.     

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible competitive inhibitor, tested by simulated progress curves

The use of suicide substrates remains a very important and useful method in enzymology for studying enzyme mechanisms and designing potential drugs. Suicide substrates act as modified substrates for the target enzymes and bind to the active site. Therefore the presence of a competitive reversible inhibitor decreases the rate of substrate-induced inactivation and protects the enzyme from this inactivation. This lowering on the inactivation rate has evident physiological advantages, since it allows the easy acquisition of experimental data and facilitates kinetic data analysis by providing another variable (inhibitor concentration). However despite the importance of the simultaneous action of a suicide substrate and a competitive reversible inhibition, to date no corresponding kinetic analysis has been carried out. Therefore we present a general kinetic analysis of a Michaelis-Menten reaction mechanism with double inhibition caused by both, a suicide substrate and a competitive reversible inhibitor. We assume rapid equilibrium of the reversible reaction steps involved, while the time course equations for the reaction product have been derived with the assumption of a limiting enzyme. The goodness of the analytical solutions has been tested by comparison with the simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested. In conclusion, we present a complete kinetic analysis of an enzyme reaction mechanism as described above in an attempt to fill a gap in the theoretical treatment of this type of system.     

Transient model of thermal deactivation of enzymes

The kinetics of enzyme deactivation provide useful insights on processes that determine the level of biological function of any enzyme. Photinus pyralis (firefly) luciferase is a convenient enzyme system for studying mechanisms and kinetics of enzyme deactivation, refolding, and denaturation caused by various external factors, physical or chemical by nature. In this report we present a study of luciferase deactivation caused by increased temperature (i.e., thermal deactivation). We found that deactivation occurs through a reversible intermediate state and can be described by a Transient model that includes active and reversibly inactive states. The model can be used as a general framework for analysis of complex, multiexponential transient kinetics that can be observed for some enzymes by reaction progression assays. In this study the Transient model has been used to develop an analytical model for studying a time course of luciferase deactivation. The model might be applicable toward enzymes in general and can be used to determine if the enzyme exposed to external factors, physical or chemical by nature, undergoes structural transformation consistent with thermal mechanisms of deactivation.     

How methionyl-tRNA synthetase creates its amino acid recognition pocket upon L-methionine binding

Amino acid selection by aminoacyl-tRNA synthetases requires efficient mechanisms to avoid incorrect charging of the cognate tRNAs. A proofreading mechanism prevents Escherichia coli methionyl-tRNA synthetase (EcMet-RS) from activating in vivo L-homocysteine, a natural competitor of L-methionine recognised by the enzyme. The crystal structure of the complex between EcMet-RS and L-methionine solved at 1.8 A resolution exhibits some conspicuous differences with the recently published free enzyme structure. Thus, the methionine delta-sulphur atom replaces a water molecule H-bonded to Leu13N and Tyr260O(eta) in the free enzyme. Rearrangements of aromatic residues enable the protein to form a hydrophobic pocket around the ligand side-chain. The subsequent formation of an extended water molecule network contributes to relative displacements, up to 3 A, of several domains of the protein. The structure of this complex supports a plausible mechanism for the selection of L-methionine versus L-homocysteine and suggests the possibility of information transfer between the different functional domains of the enzyme.     

A kinetic view of clathrin assembly and endocytic cargo sorting

Specificity and sensitivity in biochemical reactions can be achieved through regulation of equilibrium binding affinity or through proofreading mechanisms that allow for the dissociation of unwanted intermediates. In this essay, we aim to provide our perspectives on how the concept of kinetic proofreading might apply in the context of cargo sorting in clathrin-mediated endocytosis.     

DNA polymerase mutagenic bypass and proofreading of endogenous DNA lesions

DNA polymerases differentiate between correct and incorrect substrates during synthesis on undamaged DNA templates through the biochemical steps of base incorporation, primer-template extension and proofreading excision. Recent research examining DNA polymerase processing of abasic, alkylation and oxidative lesions is reviewed in light of these discrimination mechanisms. Inhibition of DNA synthesis results from correct polymerase discrimination against utilization of geometrically incorrect template bases or 3' terminal basepairs. The efficiency of translesion synthesis is thus related to the physical structure of the lesion containing DNA. However, variations in enzyme structure and kinetics result in translesion synthesis efficiencies that are also dependent upon the DNA polymerase. With a low probability, polymerase misinsertion events create a 3' lesion terminus which is geometrically favored over the correct lesion basepair, resulting in mutagenic translesion synthesis. For example, both polymerase alpha and polymerase beta appear to require the formation of a stable 3' primer-template structure for efficient abasic site translesion synthesis. However, the enzymes differ as to the precise molecular make-up of the stable DNA structure, resulting in different mutational specificities. Similar mechanisms may be applicable to oxidative damage, where mutational specificities dependent upon the DNA polymerase also have been observed. In vitro reaction conditions also influence DNA polymerase processing of lesions. Using an in vitro herpes simplex virus thymidine kinase (HSV-tk) gene forward mutation assay, we demonstrate that high dNTP substrate concentrations affect the mutagenic specificity of translesion synthesis using alkylated templates. The exonuclease-deficient Klenow polymerase error frequency for G-->A transition mutations using templates modified by N-ethyl-N-nitrosourea (ENU) was four-fold higher at 1000 microM [dNTP], relative to 50 microM [dNTP], consistent with an increased efficiency of extension of the etO6G.T mispair. Moreover, the frequency of other ENU-induced polymerase errors was suppressed when polymerase reactions contained 50 microM dNTP, relative to 1000 microM dNTP. The efficiency of proofreading as a polymerase error discrimination mechanism reflects a balance between the competing processes of 3'-->5' exonuclease removal of mispairs and polymerization of the next correct nucleotide. Polymerases that are devoid of a proofreading exonuclease generally display enhanced abasic site translesion synthesis relative to proofreading-proficient enzymes. In addition, the proofreading exonucleases of Escherichia coli Pol I and T4 DNA polymerases have been found to remove mispairs caused by abasic sites and oxidative lesions, respectively, resulting in lowered polymerase error rates. However, the magnitude of the exonuclease effect is small (less than 10-fold), and highly dependent upon the DNA polymerase-exonuclease. We have studied proofreading exonuclease removal of alkylation damage in the HSV-tk forward assay. We observed no significant reduction in the magnitude of the mutant frequency vs. dose-response curves when N-methyl-N-nitrosourea or ENU-treated templates were used in exonuclease-proficient Klenow polymerase reactions, as compared to the exonuclease-deficient polymerase reactions. Thus, available data suggest that proofreading excision of endogenous lesion mispairs does occur, but the efficiency is dependent upon the lesion and the DNA polymerase-exonuclease studied.     

Understanding the Functional Roles of Amino Acid Residues in Enzyme Catalysis

The MACiE database contains 223 distinct step-wise enzyme reaction mechanisms and holds representatives from each EC sub-subclass where there is a crystal structure and sufficient evidence in the literature to support a mechanism. Each catalytic step of every reaction sequence in MACiE is fully annotated so that it includes the function of the catalytic residues involved in the reaction and the mechanism by which substrates are transformed into products. Using MACiE as a knowledge base, we have seen that the top 10 most catalytic residues are histidine, aspartate, glutamate, lysine, cysteine, arginine, serine, threonine, tyrosine and tryptophan. Of these only seven (cysteine, histidine, aspartate, lysine, serine, threonine and tyrosine) dominate catalysis and provide essentially five functional roles that are essential. Stabilisation is the most common and essential role for all classes of enzyme, followed by general acid/base (proton acceptor and proton donor) functionality, with nucleophilic addition following closely behind (nucleophile and nucleofuge). We investigated the occurrence of these residues in MACiE and the Catalytic Site Atlas and found that, as expected, certain residue types are associated with each functional role, with some residue types able to perform diverse roles. In addition, it was seen that different EC classes of enzyme have a tendency to employ different residues for catalysis. Further, we show that whilst the differences between EC classes in catalytic residue composition are not immediately obvious from the general classes of Ingold mechanisms, there is some weak correlation between the mechanisms involved in a given EC class and the functions that the catalytic amino acid residues are performing. The analysis presented here provides a valuable insight into the functional roles of catalytic amino acid residues, which may have applications in many aspects of enzymology, from the design of novel enzymes to the prediction and validation of enzyme reaction mechanisms.     

Global dynamic optimization approach to predict activation in metabolic pathways

Background

During the last decade, a number of authors have shown that the genetic regulation of metabolic networks may follow optimality principles. Optimal control theory has been succesfully used to compute optimal enzyme profiles considering simple metabolic pathways. However, applying this optimal control framework to more general networks (e.g. branched networks, or networks incorporating enzyme production dynamics) yields problems that are analytically intractable and/or numerically very challenging. Further, these previous studies have only considered a single-objective framework.

Results

In this work we consider a more general multi-objective formulation and we present solutions based on recent developments in global dynamic optimization techniques. We illustrate the performance and capabilities of these techniques considering two sets of problems. First, we consider a set of single-objective examples of increasing complexity taken from the recent literature. We analyze the multimodal character of the associated non linear optimization problems, and we also evaluate different global optimization approaches in terms of numerical robustness, efficiency and scalability. Second, we consider generalized multi-objective formulations for several examples, and we show how this framework results in more biologically meaningful results.

Conclusions

The proposed strategy was used to solve a set of single-objective case studies related to unbranched and branched metabolic networks of different levels of complexity. All problems were successfully solved in reasonable computation times with our global dynamic optimization approach, reaching solutions which were comparable or better than those reported in previous literature. Further, we considered, for the first time, multi-objective formulations, illustrating how activation in metabolic pathways can be explained in terms of the best trade-offs between conflicting objectives. This new methodology can be applied to metabolic networks with arbitrary topologies, non-linear dynamics and constraints.     

Trans-oligomerization of duplicated aminoacyl-tRNA synthetases maintains genetic code fidelity under stress

Aminoacyl-tRNA synthetases (aaRSs) play a key role in deciphering the genetic message by producing charged tRNAs and are equipped with proofreading mechanisms to ensure correct pairing of tRNAs with their cognate amino acid. Duplicated aaRSs are very frequent in Nature, with 25,913 cases observed in 26,837 genomes. The oligomeric nature of many aaRSs raises the question of how the functioning and oligomerization of duplicated enzymes is organized. We characterized this issue in a model prokaryotic organism that expresses two different threonyl-tRNA synthetases, responsible for Thr-tRNA^Thr synthesis: one accurate and constitutively expressed (T1) and another (T2) with impaired proofreading activity that also generates mischarged Ser-tRNA^Thr. Low zinc promotes dissociation of dimeric T1 into monomers deprived of aminoacylation activity and simultaneous induction of T2, which is active for aminoacylation under low zinc. T2 either forms homodimers or heterodimerizes with T1 subunits that provide essential proofreading activity in trans. These findings evidence that in organisms with duplicated genes, cells can orchestrate the assemblage of aaRSs oligomers that meet the necessities of the cell in each situation. We propose that controlled oligomerization of duplicated aaRSs is an adaptive mechanism that can potentially be expanded to the plethora of organisms with duplicated oligomeric aaRSs.