Two-Dimensional Reaction Free Energy Surfaces of Catalytic Reaction:  Effects of Protein Conformational Dynamics on Enzyme Catalysis

Despite growing evidence suggesting the importance of enzyme conformational dynamics (ECD) in catalysis, a consensus on how precisely ECD influences the chemical step and reaction rates is yet to be reached. Here, we characterize ECD in Cyclophilin A, a well-studied peptidyl-prolyl cis-trans isomerase, using normal and accelerated, atomistic molecular dynamics simulations. Kinetics and free energy landscape of the isomerization reaction in solution and enzyme are explored in unconstrained simulations by allowing significantly lower torsional barriers, but in no way compromising the atomistic description of the system or the explicit solvent. We reveal that the reaction dynamics is intricately coupled to enzymatic motions that span multiple timescales and the enzyme modes are selected based on the energy barrier of the chemical step. We show that Kramers' rate theory can be used to present a clear rationale of how ECD affects the reaction dynamics and catalytic rates. The effects of ECD can be incorporated into the effective diffusion coefficient, which we estimate to be about ten times slower in enzyme than in solution. ECD thereby alters the preexponential factor, effectively impeding the rate enhancement. From our analyses, the trend observed for lower torsional barriers can be extrapolated to actual isomerization barriers, allowing successful prediction of the speedup in rates in the presence of CypA, which is in notable agreement with experimental estimates. Our results further reaffirm transition state stabilization as the main effect in enhancing chemical rates and provide a unified view of ECD's role in catalysis from an atomistic perspective.cis-trans isomerization | Cyclophilin A | enzyme catalysis | enzyme dynamics | Kramers' rate theory E nzymes accelerate reaction rates by several orders of magnitude, allowing them to occur at timescales relevant for cellular functions (1). One of the long-standing issues in biochemistry is how enzymes achieve this remarkable speedup. It is commonly accepted that the most dominating effect arises from significant reduction in the free energy barrier compared to the corresponding noncatalyzed reaction in solution. It is also well established that this predominant effect is mainly electrostatic in nature (2, 3), which is more favorable for the transition state than the reactant or the product (1). However, to what degree and how other factors such as desolvation, steric strain, and enzyme dynamics contribute to catalysis remains disputable. Of particular interest is the role of enzyme dynamics in catalysis that has stirred considerable debate (4-11) partly because it has not been clearly defined, leading to a semantic issue. Also, the link between enzyme dynamics and catalysis is difficult to address both experimentally and theoretically. Currently, the implications of enzyme dynamics are from ensemble-and time-averaged experiments, as the temporal behavior of every atom cannot be observed directly. Although standard molecular dynamics (MD) simulations can provide an a...

Section: Using Kramers' Rate Theory To Explain the Effects Of Cypa Dymentioning

confidence: 82%

Resolving the complex role of enzyme conformational dynamics in catalytic function

Doshi

McGowan

Ladani

et al. 2012

“…Finally, we mention that recently there has been increasing discussion of the fact that reactions that in the past had been described in terms of a one-dimensional FES [e.g., enzymatic reactions (34) or the analysis of single-molecule experiments (35)] in fact require more than one dimension for a valid description. Although we have illustrated the present methodology by applying it to protein folding, we note that the approach is perfectly general.…”

Section: Concluding Discussionmentioning

confidence: 99%

Diffusive reaction dynamics on invariant free energy profiles

Krivov

Karplus

2008

119

192

A fundamental problem in the analysis of protein folding and other complex reactions in which the entropy plays an important role is the determination of the activation free energy from experimental measurements or computer simulations. This article shows how to combine minimum-cut-based free energy profiles (F C), obtained from equilibrium molecular dynamics simulations, with conventional histogram-based free energy profiles (F H) to extract the coordinatedependent diffusion coefficient on the F C (i.e., the method determines free energies and a diffusive preexponential factor along an appropriate reaction coordinate). The F C, in contrast to the FH, is shown to be invariant with respect to arbitrary transformations of the reaction coordinate, which makes possible partition of configuration space into basins in an invariant way. A ''natural coordinate,'' for which F H and FC differ by a multiplicative constant (constant diffusion coefficient), is introduced. The approach is illustrated by a model onedimensional system, the alanine dipeptide, and the folding reaction of a double ␤-hairpin miniprotein. It is shown how the results can be used to test whether the putative reaction coordinate is a good reaction coordinate.diffusion ͉ protein folding ͉ one-dimensional free energy surfaces ͉ variable diffusion coefficient F ree energy surface (FES) projected on a few progress variables (usually one or two) is often used to describe the equilibrium and kinetic properties of complex systems with a very large number (100 to 1,000 or more) of degrees of freedom. Studies of protein folding are an important example where this type of projected surface has been introduced and progress variables such as the number of native contacts and radius of gyration have been used (1-3). Most experimental analyses of protein folding have used a related approach; for example, if the distribution of folding times is exponential, it is assumed that there is a single free energy barrier along a generally unknown one-dimensional reaction coordinate. For a few systems that show more complex kinetics, the results have been interpreted in terms of projected FESs in two dimensions (4), although, again, the actual progress variables are not known. However, even when a one-dimensional single-barrier free energy projection seems adequate to describe the kinetics, there is a fundamental difficulty in determining the barrier height, because the measurements provide only one parameter (e.g., in protein folding, the rate constant of the corresponding unimolecular reaction is obtained). In such a standard ''one-dimensional'' analysis, the rate constant, k, is written as k ϭ k 0 e Ϫ⌬F/kT , where k 0 is the preexponential factor and ⌬F is the free energy of activation. Thus, there are two unknowns, k 0 and ⌬F, to be determined from one measurement. For many small-molecule reactions, the entropic contribution to the barrier is negligible (⌬F Ϸ ⌬E, the activation energy), so that a measurement of the temperature dependence of the reaction rate can be used t...

“…In the next step, we proceeded to examine the intriguing proposal that the chemical reaction is partly driven by the kinetic energy that is associated with the conformational change, which is in turn triggered by the binding of the substrate (17). This study started by taking the 2-D model and artificially increasing the energy of the open state, thus simulating a very exothermic binding process.…”

Section: Exploring the Idea That Dynamical Coupling Contributes To Camentioning

confidence: 99%

Enzyme millisecond conformational dynamics do not catalyze the chemical step

Pisliakov

Cao

Kamerlin

et al. 2009

200

220

The idea that enzymes catalyze reactions by dynamical coupling between the conformational motions and the chemical coordinates has recently attracted major experimental and theoretical interest. However, experimental studies have not directly established that the conformational motions transfer energy to the chemical coordinate, and simulating enzyme catalysis on the relevant timescales has been impractical. Here, we introduce a renormalization approach that transforms the energetics and dynamics of the enzyme to an equivalent low-dimensional system, and allows us to simulate the dynamical coupling on a ms timescale. The simulations establish, by means of several independent approaches, that the conformational dynamics is not remembered during the chemical step and does not contribute significantly to catalysis. Nevertheless, the precise nature of this coupling is a question of great importance.adenylate kinase ͉ coarse-grained model ͉ renormalization ͉ simplified model ͉ enzyme catalysis