Origin of the Non-Arrhenius Behavior of the Rates of Enzymatic Reactions

A structural perspective on the temperature-dependent activity of enzymes

Enzymes are biomolecular catalysts whose activity varies with temperature. Unlike for small-molecule catalysts, the structural ensembles of enzymes can vary substantially with temperature, and it is in general unclear how this modulates the temperature dependence of activity. Here multi-temperature X-ray crystallography was used to record structural changes from -20°C to 40°C for a mesophilic enzyme in complex with inhibitors mimicking substrate-, intermediate-, and product-bound states, representative of major complexes underlying the kinetic constantk c a t . Both inhibitors, substrates and catalytically relevant loop motifs increasingly populate catalytically competent conformations as temperature increases. These changes occur even in temperature ranges where kinetic measurements show roughly linear Arrhenius/Eyring behavior where parameters characterizing the system are assumed to be temperature independent. Simple analysis shows that linear Arrhenius/Eyring behavior can still be observed when the underlying activation energy / enthalpy values vary with temperature, e.g., due to structural changes, and that the underlying thermodynamic parameters can be far from values derived from Arrhenius/Eyring model fits. Our results indicate a critical role for temperature-dependent atomic-resolution structural data in interpreting temperature-dependent kinetic data from enzymatic systems.

Cooperative Conformational Transitions Underpin the Activation Heat Capacity in the Temperature Dependence of Enzyme Catalysis

Many enzymes display non-Arrhenius behavior with curved Arrhenius plots in the absence of denaturation. There has been significant debate about the origin of this behavior and recently the role of the activation heat capacity (ΔCP⧧) has been widely discussed. If enzyme-catalyzed reactions occur with appreciable negative values of ΔCP⧧ (arising from narrowing of the conformational space along the reaction coordinate), then curved Arrhenius plots are a consequence. To investigate these phenomena in detail, we have collected high precision temperature-rate data over a wide temperature interval for a model glycosidase enzyme MalL, and a series of mutants that change the temperature-dependence of the enzyme-catalyzed rate. We use these data to test a range of models including macromolecular rate theory (MMRT) and an equilibrium model. In addition, we have performed extensive molecular dynamics (MD) simulations to characterize the conformational landscape traversed by MalL in the enzyme-substrate complex and an enzyme-transition state complex. We have crystallized the enzyme in a transition state-like conformation in the absence of a ligand and determined an X-ray crystal structure at very high resolution (1.10 Å). We show (using simulation) that this enzyme-transition state conformation has a more restricted conformational landscape than the wildtype enzyme. We coin the term "transition state-like conformation (TLC)" to apply to this state of the enzyme. Together, these results imply a cooperative conformational transition between an enzyme-substrate conformation (ES) and a transition-state-like conformation (TLC) that precedes the chemical step. We present a two-state model as an extension of MMRT (MMRT-2S) that describes the data along with a convenient approximation with linear temperature dependence of the activation heat capacity (MMRT-1L) that can be used where fewer data points are available. Our model rationalizes disparate behavior seen for MalL and previous results for a thermophilic alcohol dehydrogenase and is consistent with a raft of data for other enzymes. Our model can be used to characterize the conformational changes required for enzyme catalysis and provides insights into the role of cooperative conformational changes in transition state stabilization that are accompanied by changes in heat capacity for the system along the reaction coordinate. TLCs are likely to be of wide importance in understanding the temperature dependence of enzyme activity and other aspects of enzyme catalysis.

Evolution of Optimized Hydride Transfer Reaction and Overall Enzyme Turnover in Human Dihydrofolate Reductase

Evolution of dihydrofolate reductase (DHFR) has been studied using the enzyme from Escherichia coli DHFR (ecDHFR) as a model, but less studies have used the enzyme from Homo sapiens DHFR (hsDHFR). Each enzyme maintains a short and narrow distribution of hydride donor-acceptor distances (DAD) at the tunneling ready state (TRS). Evolution of the enzyme was previously studied in ecDHFR where three key sites were identified as important to the catalyzed reaction. The corresponding sites in hsDHFR are F28, 62-PEKN, and 26-PPLR. Each of these sites was studied here through the creation of mutant variants of the enzyme and measurements of the temperature dependence of the intrinsic kinetic isotope effects (KIEs) on the reaction. F28 is mutated first to M (F28M) and then to the L of the bacterial enzyme (F28L). The KIEs of the F28M variant are larger and more temperature-dependent than wild-type (WT), suggesting a broader and longer average DAD at the TRS. To more fully mimic ecDHFR, we also study a triple mutant of the human enzyme (F32L-PP26N-PEKN62G). Remarkably, the intrinsic KIEs, while larger in magnitude, are temperature-independent like the WT enzymes. We also construct deletion mutations of hsDHFR removing both the 62-PEKN and 26-PPLR sequences. The results mirror those described previously for insertion mutants of ecDHFR. Taken together, these results suggest a balancing act during DHFR evolution between achieving an optimal TRS for hydride transfer and preventing product inhibition arising from the different intercellular pools of NADPH and NADP⁺ in prokaryotic and eukaryotic cells.

Use of confocal Raman microscopy to characterise ethyl cyanoacrylate adhesive depth curing

In situ spatial temporal measurement of monomer conversion during adhesive bondline curing remains a challenging area. The aim of this work was to demonstrate the effectiveness of using confocal Raman microscopy in a specially configured experimental set-up, as a versatile tool for measuring monomer concentration changes as a function of both time and adhesive bond depth during ethyl cyanoacrylate polymerisation. This also allowed monitoring of the extent of polymerisation at the adhesive substrate interface independently of the bulk bondline polymerisation region. Key kinetic parameters such as inhibition time t_lag, rate of reaction R_max and extent of reaction [α_t]_max were obtained by fitting the experimental data to sigmoidal growth curves using simple piecewise regression models. A systematic characterisation of a polymerisation reaction was conducted using different sample substrate types (copper alloy (red brass), aluminium, aluminium alloy, stainless steel and borosilicate glass) and at various reaction temperatures. Reaction rates were found to decrease further away from the substrate interface in the bulk volume region. The fastest kinetics occurred in the vicinity of nucleophilic hydroxyl rich surfaces such as at the copper alloy (red brass). In addition to substrate surface chemistry, surface roughness was also a factor, with the highest reaction rates occurring with a grit blasted (roughened) aluminium alloy (2024 T3) surface. An approximately linear dependence of the ln R_maxvs. 1/T (Arrhenius) plot was recorded within the temperature range of 291-328 K. A better fit was obtained however through the use of two separate linear slopes, possibly indicative of a change of polymerisation reaction mechanism taking place at elevated temperatures with two distinct activation energies. Further work conducted using a larger number of temperatures would be useful to verify this finding. This work confirmed that differences in the rates of interfacial and bulk polymerisation processes could be readily measured in situ using confocal Raman microscopy which is a powerful technique for investigating such surface-confined and bulk polymerisation reactions.

Hidden Conformational States and Strange Temperature Optima in Enzyme Catalysis

The existence of temperature optima in enzyme catalysis that occur before protein melting sets in can be described by different types of kinetic models. Such optima cause distinctly curved Arrhenius plots and have, for example, been observed in several cold-adapted enzymes from psychrophilic species. The two main explanations proposed for this behavior either invoke conformational equilibria with inactive substrate-bound states or postulate differences in heat capacity between the reactant and transition states. Herein, we analyze the implications of the different types of kinetic models in terms of apparent activation enthalpies, entropies, and heat capacities, using the catalytic reaction of a cold-adapted α-amylase as a prototypic example. We show that the behavior of these thermodynamic activation parameters is fundamentally different between equilibrium and heat capacity models, and in the α-amylase case, computer simulations have shown the former model to be correct. A few other enzyme-catalyzed reactions are also discussed in this context.

Temperature, Dynamics, and Enzyme-Catalyzed Reaction Rates

We review the adaptations of enzyme activity to different temperatures. Psychrophilic (cold-adapted) enzymes show significantly different activation parameters (lower activation enthalpies and entropies) from their mesophilic counterparts. Furthermore, there is increasing evidence that the temperature dependence of many enzyme-catalyzed reactions is more complex than is widely believed. Many enzymes show curvature in plots of activity versus temperature that is not accounted for by denaturation or unfolding. This is explained by macromolecular rate theory: A negative activation heat capacity for the rate-limiting chemical step leads directly to predictions of temperature optima; both entropy and enthalpy are temperature dependent. Fluctuations in the transition state ensemble are reduced compared to the ground state. We show how investigations combining experiment with molecular simulation are revealing fundamental details of enzyme thermoadaptation that are relevant for understanding aspects of enzyme evolution. Simulations can calculate relevant thermodynamic properties (such as activation enthalpies, entropies, and heat capacities) and reveal the molecular mechanisms underlying experimentally observed behavior.

Conformational sampling and kinetics changes across a non-Arrhenius break point in the enzyme thermolysin

Numerous studies have suggested a significant role that protein dynamics play in optimizing enzyme catalysis, and changes in conformational sampling offer a window to explore this role. Thermolysin from Bacillus thermoproteolyticus rokko, which is a heat-stable zinc metalloproteinase, serves here as a model system to study changes of protein function and conformational sampling across a temperature range of 16-36 °C. The temperature dependence of kinetics of thermolysin showed a biphasic transition at 26 °C that points to potential conformational and dynamic differences across this temperature. The non-Arrhenius behavior observed resembled results from previous studies of a thermophilic alcohol dehydrogenase enzyme, which also indicated a biphasic transition at ambient temperatures. To explore the non-Arrhenius behavior of thermolysin, room temperature crystallography was applied to characterize structural changes in a temperature range across the biphasic transition temperature. The alternate conformation of side chain fitting to electron density of a group of residues showed a higher variability in the temperature range from 26 to 29 °C, which indicated a change in conformational sampling that correlated with the non-Arrhenius break point.

Characterization of the non-Arrhenius behavior of supercooled liquids by modeling nonadditive stochastic systems

The characterization of the formation mechanisms of amorphous solids is a large avenue for research, since understanding its non-Arrhenius behavior is challenging to overcome. In this context, we present one path toward modeling the diffusive processes in supercooled liquids near glass transition through a class of nonhomogeneous continuity equations, providing a consistent theoretical basis for the physical interpretation of its non-Arrhenius behavior. More precisely, we obtain the generalized drag and diffusion coefficients that allow us to model a wide range of non-Arrhenius processes. This provides a reliable measurement of the degree of fragility of the system and an estimation of the fragile-to-strong transition in glass-forming liquids, as well as a generalized Stokes-Einstein equation, leading to a better understanding of the classical and quantum effects on the dynamics of nonadditive stochastic systems.

Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity

Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a "d-TST" formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena.

Probing the Entropic Effect in Molecular Noncovalent Interactions between Resin-Bound Polybrominated Arenes and Small Substrates

The associative interaction between resin-bound polybrominated arenes and small molecules was analyzed by using various spectroscopic techniques as well as a synthetic molecular model to establish the thermodynamics. The binding in acetonitrile was three orders of magnitude stronger than that in methanol, partly owing to the tertiary conformational gating of the resin that controls the entropic terms. By using the entropic superiority, the associative binding of up to 3×10⁴  m^-1 is achieved with the non-biological system. A modified Hill plot for the quantitative analysis of bindings was also devised, which enabled the interactions at the molecular level to be elucidated.

Glutamine Hydrolysis by Imidazole Glycerol Phosphate Synthase Displays Temperature Dependent Allosteric Activation

The enzyme imidazole glycerol phosphate synthase (IGPS) is a model for studies of long-range allosteric regulation in enzymes. Binding of the allosteric effector ligand N'-[5'-phosphoribulosyl)formimino]-5-aminoimidazole-4-carboxamide-ribonucleotide (PRFAR) stimulates millisecond (ms) timescale motions in IGPS that enhance its catalytic function. We studied the effect of temperature on these critical conformational motions and the catalytic mechanism of IGPS from the hyperthermophile Thermatoga maritima in an effort to understand temperature-dependent allostery. Enzyme kinetic and NMR dynamics measurements show that apo and PRFAR-activated IGPS respond differently to changes in temperature. Multiple-quantum Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments performed at 303, 323, and 343 K (30, 50, and 70°C) reveal that millisecond flexibility is enhanced to a higher degree in apo IGPS than in the PRFAR-bound enzyme as the sample temperature is raised. We find that the flexibility of the apo enzyme is nearly identical to that of its PRFAR activated state at 343 K, whereas conformational motions are considerably different between these two forms of the enzyme at room temperature. Arrhenius analyses of these flexible sites show a varied range of activation energies that loosely correlate to allosteric communities identified by computational methods and reflect local changes in dynamics that may facilitate conformational sampling of the active conformation. In addition, kinetic assays indicate that allosteric activation by PRFAR decreases to 65-fold at 343 K, compared to 4,200-fold at 303 K, which mirrors the decreased effect of PRFAR on ms motions relative to the unactivated enzyme. These studies indicate that at the growth temperature of T. maritima, PFRAR is a weaker allosteric activator than it is at room temperature and illustrate that the allosteric mechanism of IGPS is temperature dependent.