Common enzymological experiments allow free energy profile determination

Theoretical Improvements in Enzyme Efficiency Associated with Noisy Rate Constants and Increased Dissipation

Previous studies have revealed the extraordinarily large catalytic efficiency of some enzymes. High catalytic proficiency is an essential accomplishment of biological evolution. Natural selection led to the increased turnover number, kcat, and enzyme efficiency, kcat/KM, of uni-uni enzymes, which convert a single substrate into a single product. We added or multiplied random noise with chosen rate constants to explore the correlation between dissipation and catalytic efficiency for ten enzymes: beta-galactosidase, glucose isomerase, β-lactamases from three bacterial strains, ketosteroid isomerase, triosephosphate isomerase, and carbonic anhydrase I, II, and T200H. Our results highlight the role of biological evolution in accelerating thermodynamic evolution. The catalytic performance of these enzymes is proportional to overall entropy production-the main parameter from irreversible thermodynamics. That parameter is also proportional to the evolutionary distance of β-lactamases PC1, RTEM, and Lac-1 when natural or artificial evolution produces the optimal or maximal possible catalytic efficiency. De novo enzyme design and attempts to speed up the rate-limiting catalytic steps may profit from the described connection between kinetics and thermodynamics.

Metaheuristics for pharmacometrics

Metaheuristics is a powerful optimization tool that is increasingly used across disciplines to tackle general purpose optimization problems. Nature-inspired metaheuristic algorithms is a subclass of metaheuristic algorithms and have been shown to be particularly flexible and useful in solving complicated optimization problems in computer science and engineering. A common practice with metaheuristics is to hybridize it with another suitably chosen algorithm for enhanced performance. This paper reviews metaheuristic algorithms and demonstrates some of its utility in tackling pharmacometric problems. Specifically, we provide three applications using one of its most celebrated members, particle swarm optimization (PSO), and show that PSO can effectively estimate parameters in complicated nonlinear mixed-effects models and to gain insights into statistical identifiability issues in a complex compartment model. In the third application, we demonstrate how to hybridize PSO with sparse grid, which is an often-used technique to evaluate high dimensional integrals, to search for D -efficient designs for estimating parameters in nonlinear mixed-effects models with a count outcome. We also show the proposed hybrid algorithm outperforms its competitors when sparse grid is replaced by its competitor, adaptive gaussian quadrature to approximate the integral, or when PSO is replaced by three notable nature-inspired metaheuristic algorithms.

Evolution of Enzyme Function and the Development of Catalytic Efficiency: Triosephosphate Isomerase, Jeremy R. Knowles, and W. John Albery

Every reader knows that an enzyme accelerates a reaction by reducing the activation-energy barrier. However, understanding how this is achieved by the structure of the enzyme and its interactions with stable complexes and transition states and, then, using this to (re)design enzymes to catalyze novel reactions remain the "holy grail" of mechanistic enzymology. The necessary foundation is the free-energy profile that specifies the energies of the bound substate, product, and intervening intermediates as well as the transition states by which they are interconverted. When this free-energy profile is compared to that for the uncatalyzed reaction, strategies for establishing and enhancing catalysis can be identified. This Perspective reminds readers that the first free-energy profile determined for an enzyme-catalyzed reaction, that for triosephosphate isomerase, was published in Biochemistry in 1976 by Jeremy R. Knowles, W. John Albery, and co-workers. They used the profile to propose three steps of increasing "subtlety" that can be influenced by evolutionary pressure to increase the flux through the reaction coordinate: (1) "uniform binding" of the substrate, product, and intermediates; (2) "differential binding" of complexes so that these are isoenergetic (to minimize the energy of the intervening transition states); and (3) "catalysis of an elementary step" in which the transition state for the kinetically significant chemical step is stabilized so that flux can be determined by the rate of substrate binding or product dissociation. These papers continue to guide mechanistic studies of enzyme-catalyzed reactions and provide principles for the (re)design of novel enzymes.

Enzyme free energy profiles: Can substrate binding be nonspontaneous? Can ground state interactions enhance catalysis?

Two influential enzymological theories were proposed in the late 1970s - that catalytic power stems only from transition state stabilization, while ground state interactions are either irrelevant or inhibitory; and enzyme substrate binding is nonspontaneous at low substrate concentrations ([S]₀ << K_m). I show here that ground state destabilization can be a very effective source of catalytic power, especially at high substrate concentrations, and enzyme-substrate binding thermodynamics are independent of initial substrate concentration. Binding free energy ranges from negative (spontaneous) under pre-steady state conditions up to a maximum of zero at steady state. Nonspontaneous binding can only occur under standard state conditions when c° is defined to be less than K_m.

The role of Brønsted base basicity in estimating carbon acidity at enzyme active sites: a caveat

Many enzymes catalyze the abstraction of a proton from a carbon acid substrate to initiate a variety of reactions; however, the development of a complete quantitative description of enzyme-catalyzed heterolytic cleavage of a C-H bond remains a challenge to enzymologists. To determine the pK value for such substrates bound at the active site, recent studies have estimated the equilibrium for formation of the deprotonated intermediate at the active site, however, accurate knowledge of the pK of the conjugate acid of the Brønsted base catalyst (BH⁺) is also required. Herein, it is shown that using the value of pK of the enzyme-substrate complex can underestimate the value of pK by an amount between zero and pδ, where pδ is the change in basicity of BH⁺ upon going from the enzyme-substrate complex to the enzyme-intermediate complex.

Carbon Acidity in Enzyme Active Sites

The pK_a values for substrates acting as carbon acids (i.e., C-H deprotonation reactions) in several enzyme active sites are presented. The information needed to calculate them includes the pK_a of the active site acid/base catalyst and the equilibrium constant for the deprotonation step. Carbon acidity is obtained from the relation pK_eq = pKar–pKap = ΔpK_a for a proton transfer reaction. Five enzymatic free energy profiles (FEPs) were calculated to obtain the equilibrium constants for proton transfer from carbon in the active site, and six additional proton transfer equilibrium constants were extracted from data available in the literature, allowing substrate C-H pK_as to be calculated for 11 enzymes. Active site-bound substrate C-H pK_a values range from 5.6 for ketosteroid isomerase to 16 for proline racemase. Compared to values in water, enzymes lower substrate C-H pK_as by up to 23 units, corresponding to 31 kcal/mol of carbanion stabilization energy. Calculation of Marcus intrinsic barriers (ΔG0‡) for pairs of non-enzymatic/enzymatic reactions shows significant reductions in ΔG0‡ for cofactor-independent enzymes, while pyridoxal phosphate dependent enzymes appear to increase ΔG0‡ to a small extent as a consequence of carbanion resonance stabilization. The large increases in carbon acidity found here are central to the large rate enhancements observed in enzymes that catalyze carbon deprotonation.

Extracting Kinetic Isotope Effects From a Global Analysis of Reaction Progress Curves

Enzyme reaction progress curves, or time course datasets, are often rich in information, yet their analysis typically reduces their information content to a single parameter, the initial velocity. An alternative approach is described here, where the time course is described by a model constructed from rate equations. In combination with global nonlinear regression, intrinsic rate and/or equilibrium constants can be directly obtained by fitting these data. This method can be greatly enhanced when combined with the measurement of (usually deuterium) isotope effects, which selectively perturb individual step(s) within the reaction, allowing better separation of fitted parameters and more robust model testing. This chapter focuses on practical considerations when using analytical and/or numerically integrated rate equations to model enzyme reactions. The emphasis is on the underlying methodology, which is demonstrated with specific examples alongside recommendations of suitable software.

Is the catalytic activity of triosephosphate isomerase fully optimized? An investigation based on maximization of entropy production

Triosephosphate isomerase (TIM) is often described as a fully evolved housekeeping enzyme with near-maximal possible reaction rate. The assumption that an enzyme is perfectly evolved has not been easy to confirm or refute. In this paper, we use maximization of entropy production within known constraints to examine this assumption by calculating steady-state cyclic flux, corresponding entropy production, and catalytic activity in a reversible four-state scheme of TIM functional states. The maximal entropy production (MaxEP) requirement for any of the first three transitions between TIM functional states leads to decreased total entropy production. Only the MaxEP requirement for the product (R-glyceraldehyde-3-phosphate) release step led to a 30% increase in enzyme activity, specificity constant kcat/KM, and overall entropy production. The product release step, due to the TIM molecular machine working in the physiological direction of glycolysis, has not been identified before as the rate-limiting step by using irreversible thermodynamics. Together with structural studies, our results open the possibility for finding amino acid substitutions leading to an increased frequency of loop six opening and product release.

Effects of Glycosylation on the Enzymatic Activity and Mechanisms of Proteases

Posttranslational modifications are an important feature of most proteases in higher organisms, such as the conversion of inactive zymogens into active proteases. To date, little information is available on the role of glycosylation and functional implications for secreted proteases. Besides a stabilizing effect and protection against proteolysis, several proteases show a significant influence of glycosylation on the catalytic activity. Glycans can alter the substrate recognition, the specificity and binding affinity, as well as the turnover rates. However, there is currently no known general pattern, since glycosylation can have both stimulating and inhibiting effects on activity. Thus, a comparative analysis of individual cases with sufficient enzyme kinetic and structural data is a first approach to describe mechanistic principles that govern the effects of glycosylation on the function of proteases. The understanding of glycan functions becomes highly significant in proteomic and glycomic studies, which demonstrated that cancer-associated proteases, such as kallikrein-related peptidase 3, exhibit strongly altered glycosylation patterns in pathological cases. Such findings can contribute to a variety of future biomedical applications.