Calculation of Heat Capacity Changes in Enzyme Catalysis and Ligand Binding

A structural perspective on the temperature dependent activity of enzymes

Enzyme activity varies with temperature. Unlike small-molecule catalysts, the structural ensembles of enzymes can change substantially with temperature, but it is unclear how this modulates temperature dependent 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 on the reaction coordinate. Inhibitors, substrates and active site loops increasingly populated catalytically competent conformations as temperature increased. These changes occurred even in temperature ranges where kinetic measurements showed 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. Our results indicate a critical role for temperature dependent atomic-resolution structural data in interpreting temperature dependent kinetic data from enzymatic systems.

Computer Simulations of the Temperature Dependence of Enzyme Reactions

In this review we discuss the development of methodology for calculating the temperature dependence and thermodynamic activation parameters for chemical reactions in solution and in enzymes, from computer simulations. We outline how this is done by combining the empirical valence bond method with molecular dynamics free energy simulations. In favorable cases it turns out that such simulations can even capture temperature optima for the catalytic rate. The approach turns out be very useful both for addressing questions regarding the roles of enthalpic and entropic effects in specific enzymes and also for attacking evolutionary problems regarding enzyme adaptation to different temperature regimes. In the latter case, we focus on cold-adaptation of enzymes from psychrophilic species and show how computer simulations have revealed the basic mechanisms behind such adaptation. Understanding these mechanisms also opens up the possibility of designing the temperature dependence, and we highlight a recent example of this.

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.

Response of Foldable Protein Conformations to Non-Physiological Perturbations: Interplay of Thermal Factors and Confinement

Technological advances frequently interface biomolecules with nanomaterials at non-physiological conditions, necessitating response characterization of key processes. Similar encounters are expected in cellular contexts. We report in silico investigations of the response of diverse protein conformational states to lowering of temperature and imposition of spatial constraints. Conformational states are represented by folded form of the Albumin binding domain (ABD) protein, its compact denatured form, and structurally disordered nascent folding elements. Data from extensive simulations are evaluated to elicit structural, thermodynamic and dynamic responses of the states and their associated environment. Analyses reveal alterations to folding propensity with reduced thermal energy and confinement, with signatures of trend reversal in highly disordered states. Across temperatures, confinement has restrictive effects on volume and energetic fluctuations, leading to narrowing of differences in isothermal compressibility (κ) and heat capacities (Cp). While excess (over ideal gas) entropy of the hydration layer marks dependence on the conformational state at bulk, confinement triggers erasure of differences. These observations are largely consistent with timescales of protein-water hydrogen bonding dynamics. The results implicate multi-factorial associations within a simple bio-nano complex. We expect the current study to motivate investigations of more biologically relevant interfaces towards mechanistic understanding and potential applications.

Computational Analysis of Heat Capacity Effects in Protein-Ligand Binding

Heat capacity effects in protein-ligand binding as measured by calorimetric experiments have recently attracted considerable attention, particularly in the field of enzyme inhibitor design. A significant negative heat capacity change upon ligand binding implies a marked temperature dependence of the binding enthalpy, which is of high relevance for attempts to optimize protein-ligand interactions. In this work, we address the question of how well such heat capacity changes can be predicted by computer simulations. We examine a series of human thrombin inhibitors that all bind with ΔCp values of about -0.4 kcal/mol/K and calculate heat capacity changes from plain molecular dynamics simulations of the bound and free states of the enzyme and ligand. The results show that accurate ΔCp estimates within a few tenths of a kcal/mol/K of the experimental values can be obtained with this approach. This allows us to address the structural and energetic origin of the negative heat capacity changes for the thrombin inhibitors, and it is found that conformational equilibria of the free ligands in solution make a major contribution to the observed effect.

Interplay of structural preorganization and conformational sampling in UDP-glucuronic acid 4-epimerase catalysis

Understanding enzyme catalysis as connected to protein motions is a major challenge. Here, based on temperature kinetic studies combined with isotope effect measurements, we obtain energetic description of C-H activation in NAD-dependent UDP-glucuronic acid C4 epimerase. Approach from the ensemble-averaged ground state (GS) to the transition state-like reactive conformation (TSRC) involves, alongside uptake of heat (Δ H ‡  = 54 kJ mol-1), significant loss in entropy ( - T Δ S ‡  = 20 kJ mol-1; 298 K) and negative activation heat capacity (Δ C p ‡  = -0.64 kJ mol-1 K-1). Thermodynamic changes suggest the requirement for restricting configurational freedom at the GS to populate the TSRC. Enzyme variants affecting the electrostatic GS preorganization reveal active-site interactions important for precise TSRC sampling and H-transfer. Collectively, our study captures thermodynamic effects associated with TSRC sampling and establishes rigid positioning for C-H activation in an enzyme active site that requires conformational flexibility in fulfillment of its natural epimerase function.

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.

Model-driven insights into the effects of temperature on metabolism

Temperature affects cellular processes at different spatiotemporal scales, and identifying the genetic and molecular mechanisms underlying temperature responses paves the way to develop approaches for mitigating the effects of future climate scenarios. A systems view of the effects of temperature on cellular physiology can be obtained by focusing on metabolism since: (i) its functions depend on transcription and translation and (ii) its outcomes support organisms' development, growth, and reproduction. Here we provide a systematic review of modelling efforts directed at investigating temperature effects on properties of single biochemical reactions, system-level traits, metabolic subsystems, and whole-cell metabolism across different prokaryotes and eukaryotes. We compare and contrast computational approaches and theories that facilitate modelling of temperature effects on key properties of enzymes and their consideration in constraint-based as well as kinetic models of metabolism. In addition, we provide a summary of insights from computational approaches, facilitating integration of omics data from temperature-modulated experiments with models of metabolic networks, and review the resulting biotechnological applications. Lastly, we provide a perspective on how different types of metabolic modelling can profit from developments in machine learning and models of different cellular layers to improve model-driven insights into the effects of temperature relevant for biotechnological applications.

Computational design of the temperature optimum of an enzyme reaction

Cold-adapted enzymes are characterized both by a higher catalytic activity at low temperatures and by having their temperature optimum down-shifted, compared to mesophilic orthologs. In several cases, the optimum does not coincide with the onset of protein melting but reflects some other type of inactivation. In the psychrophilic α-amylase from an Antarctic bacterium, the inactivation is thought to originate from a specific enzyme-substrate interaction that breaks around room temperature. Here, we report a computational redesign of this enzyme aimed at shifting its temperature optimum upward. A set of mutations designed to stabilize the enzyme-substrate interaction were predicted by computer simulations of the catalytic reaction at different temperatures. The predictions were verified by kinetic experiments and crystal structures of the redesigned α-amylase, showing that the temperature optimum is indeed markedly shifted upward and that the critical surface loop controlling the temperature dependence approaches the target conformation observed in a mesophilic ortholog.