Dissecting the Allosteric Fine-Tuning of Enzyme Catalysis

Abstract

Fully understanding the mechanism of allosteric regulation in biomolecules requires separating and examining all of the involved factors. In enzyme catalysis, allosteric effector binding shifts the structure and dynamics of the active site, leading to modified energetic (e.g., energy barrier) and dynamical (e.g., diffusion coefficient) factors underlying the catalyzed reaction rate. Such modifications can be subtle and dependent on the type of allosteric effector, representing a fine-tuning of protein function. The microscopic description of allosteric regulation at the level of function-dictating factors has prospective applications in fundamental and pharmaceutical sciences, which is, however, largely missing so far. Here, we characterize the allosteric fine-tuning of enzyme catalysis, using human Pin1 as an example, by performing more than half-millisecond all-atom molecular dynamics simulations. Changes of reaction kinetics and the dictating factors, including the free energy surface along the reaction coordinate and the diffusion coefficient of the reaction dynamics, under various enzyme and allosteric effector binding conditions are examined. Our results suggest equal importance of the energetic and dynamical factors, both of which can be modulated allosterically, and the combined effect determines the final allosteric output. We also reveal the potential dynamic basis for allosteric modulation using an advanced statistical technique to detect function-related conformational dynamics. Methods developed in this work can be applied to other allosteric systems.

Figure 1

Free energy of prolyl isomerization in free and protein-bound peptides. (A) Structure of Pin1 bound with two peptides in the active site and the WW domain binding site. Pin1 is shown as cartoon color-coded by residue numbers (from red, white, to blue along the chain), whereas peptides are sticks color-coded by atom types. (B) Free energy along the isomerization reaction coordinate (ω). (C, D) Activation energy for the isomerization from trans to cis and cis to trans, respectively. Bar heights are defined by the free energy difference between the transition state (∼90°) and trans (∼180°) or cis (∼0°) in (B). (E) Free energy difference between cis and trans. See the Materials and Methods for more details of error bars.

Figure 2

Kinetics and diffusion coefficient of prolyl isomerization in free and protein-bound peptides. (A) Extrapolation of kinetics from modified potentials (filled circles) to the real V₂ (open circles) using the Kramers’ rate theory. Lines are linear fitting using the slope = 1/k_BT. Inset: more details about the fitting in the region around the modified potentials. (B, C) Predicted (logarithm of) rate constants and diffusion coefficients, respectively. See the Materials and Methods for more details of error bars.

Figure 3

Multiensemble functional mode analysis detects more function-correlated motions than principal component analysis. (A–D) “Porcupine” plots of PCA. The collective motion associated with the PC maximizing the correlation with the reaction coordinate describing the progress of isomerization (ω) is shown as red arrows on the structure of the PPIase domain (shown as cartoon). Lengths and colors of arrows, as well as the color of the structure, are scaled by the loadings of corresponding atoms in the PC axis. Arrows shorter than 1 Å are removed for clarity. Values in parentheses are the percentage of total conformational variance captured by the PC. σ, standard deviation of conformations along the PC. ρ, Pearson’s correlation coefficient between the PC and ω. The substrate’s Pro binding site is indicated by the yellow star in A. (E–H) “Porcupine” plots of collective motions detected by multiensemble FMA.

Figure 4

Multiensemble FMA detects motions highly correlated with the progress of reaction. (Top) Correlation between the functional principal component from PCA of each system and the reaction coordinate (reference prolyl ω). Each point represents a conformation from the umbrella sampling. The blue solid line is a linear regression of the data with R² shown in the label. (Bottom) Same results using the conformational coordinates mapped onto the functional mode as the abscissa.