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. 2015 Sep 8;24(11):1884–1889. doi: 10.1002/pro.2794

Electrostatic steering enhances the rate of cAMP binding to phosphodiesterase: Brownian dynamics modeling

Yu-ming M Huang 1,*, Gary Huber 2, J Andrew McCammon 1,2,3
PMCID: PMC4622220  PMID: 26346301

Abstract

Signaling in cells often involves co-localization of the signaling molecules. Most experimental evidence has shown that intracellular compartmentalization restricts the range of action of the second messenger, 3'-5'-cyclic adenosine monophosphate (cAMP), which is degraded by phosphodiesterases (PDEs). The objective of this study is to understand the details of molecular encounter that may play a role in efficient operation of the cAMP signaling apparatus. The results from electrostatic potential calculations and Brownian dynamics simulations suggest that positive potential of the active site from PDE enhances capture of diffusing cAMP molecules. This electrostatic steering between cAMP and the active site of a PDE plays a major role in the enzyme-substrate encounter, an effect that may be of significance in sequestering cAMP released from a nearby binding site or in attracting more freely diffusing cAMP molecules.

Keywords: second messenger, phosphodiesterase, protein kinase A, BrownDye simulation, electrostatic property, association rate constant

Introduction

In order to transform extracellular stimuli into adequate intracellular responses, signal transduction events occur on the cell surface when an exterior molecule activates an interior receptor, where the transmission of the molecular signals commonly requires an orchestrated response of many signaling molecules.1–3 A particularly well-known case for signaling is the second messenger, 3'-5'-cyclic adenosine monophosphate (cAMP).4 Cyclic AMP is a derivative of adenosine triphosphate and can affect a countless number of cellular functions in different organisms, such as the activation of protein kinase A (PKA), the regulation of ion channels and the phosphorylation in excitation–contraction coupling.5–8 Since the discovery of cAMP from 1950s, studies have indicated that the loss of cAMP and PKA signaling could trigger several neuronal, brain, and heart diseases9–11; hence, the enhanced understanding of the signaling pathways and colocation of the signaling molecules could help for further treatments and drug discovery.

The regulation of cAMP can be divided into the following three steps. First, after activation by G-protein-coupled receptors, adenylyl cyclases produce cAMP as a source enzyme.12,13 Second, sink enzymes, phosphodiesterases (PDEs), control degradation of cAMP and shape the cAMP gradient to propagate specific signals.14 Third, such compartmentalization allows cAMP effectors, such as PKA, being activated and generating downstream signaling events to further influence other kinase substrates tethered to A-kinase anchoring proteins (AKAPs).15,16 As a result, the threshold of activation for cAMP effectors is highly related to PDE action and cAMP concentration. An active role of PDE in regulating cAMP signals has been supported by a number of studies.17–19

Several computational studies of localized signaling have been published.20 For example, Chen et al. constructed a simplified model to quantitatively evaluate the degradation of cAMP by PDEs. The results indicated that high PDE concentration is necessary in the degradation and that PDEs are required to be localized to ensure compartmentalization in cAMP signaling.21 Oliveira et al. explored the mechanism of localized cAMP signaling including cAMP production, PKA activation, and cAMP degradation by PDE activity through stochastic modeling. The simulations further demonstrated that PDEs are directly responsible for cAMP microdomain definition and the cAMP microdomain does not require diffusional barriers.22 Although the studies have confirmed the role of cAMP, PDE and PKA in the second messenger signaling pathways, they have not attempted to model the detailed molecular interactions involved.

A recent experimental study indicated that, in some cases, very close interaction of the regulatory subunits of PKA with PDE may facilitate the release of cAMP from the former to the latter.23 However, the driving forces that cause the attraction/repulsion of cAMP from PDE and detailed interactions between the two molecules are still unexplored. Here, we begin to look at the molecular details, especially electrostatic attraction and repulsion, which may play a role in efficiently terminating cAMP signals. We find that, although both molecules carry negative net charges, the positively charged active site of a PDE enhances the rate of cAMP encounter and capture of freely diffusing cAMP molecules, due to electrostatic screening effects at physiological ionic strengths. Removing the charges on cAMP or the active site of a PDE significantly reduces the association rate constants (kon) of PDE-cAMP reactions.

Results and Discussion

Electrostatic potential of PDE

The electrostatic map from APBS calculations shows that PDE contains two highly positive regions [Fig. 1(a) and 2(a)]. One is the cAMP active site; and the other area is on the protein surface. Because the crystal study showed that no positively charged residue, such as Arg and Lys, is around the cAMP active site,24 the highly positive potential is mainly contributed by two zinc ions. This result also confirms the importance of the two cations in substrate binding to PDE suggested from early studies.25,26 In contrast to the metal cations creating positive electrostatic fields around the cAMP active site, the positive potential of the surface area can be attributed to the numerous Lys and Arg amino acids on the PDE surface [Fig. 2(b)].

Figure 1.

Figure 1

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Structure of PDE. (a) The circle indicates the active site, including two zinc ions shown as gray spheres. (b) Multiple reaction radii, applied in BD simulations, are shown as spheres.

Figure 2.

Figure 2

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Electrostatic potential map of PDE. (a) Two areas of PDE have highly positive potential. One is the cAMP active site (circle); and the other region is part of the PDE surface. (b) The circle indicates the cAMP active site, which contains 2 zinc ions, 5 His, and 2 Asp. In contrast to no positively charged residue in the active site, several Lys and Arg residues are on the protein surface.

Comparison with experiments

The Brownian dynamics (BD) simulations of PDE-cAMP association show that, for physiological pH, 0.05M ionic strength, and the reaction surface at 5.44 Å, the calculated kon is 4.18 ± 0.68 × 106 (Ms)−1, which agrees well with the experimental value, kon = 3.5 ± 0.7 × 106 (Ms)−1.27 We note that this optimal reaction radius is specific to the rigid protein model studied here. Inclusion of protein dynamics would undoubtedly require some adjustment of the reaction radius. To get a sense of how the flux of cAMP is focused into the active site, rate constants were calculated for several larger reaction radii, namely 7.00, 9.00, and 11.00 Å (Fig. 3). Although PDE has a highly positively charged area on the protein surface, we did not observe any cAMP molecule becomes confined to this charged region in our simulations. Accordingly, BD simulation with the current settings can be used to study the association of cAMP to PDE.

Figure 3.

Figure 3

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Association rate constant (kon) of cAMP binding to PDE for different ionic strengths and different reaction radius. Four conditions indicate: (1) condition 1: PDE contains two zinc ions in the cAMP active site, and cAMP has a −1 charge, (2) condition 2: PDE contains two zinc ions in the cAMP active site, and cAMP has no charge, (3) condition 3: PDE does not have metal cations in the cAMP active site, and cAMP has a −1 charge, and (4) condition 4: PDE does not have metal cations in the cAMP active site, and cAMP has no charge.

Association rate of cAMP to PDE for different ion strengths

To study if electrostatic attractions between PDE and the negatively charged cAMP enhance the encounter rate of the two molecules, we predicted kon of the following four conditions: (1) condition 1: keep two zinc ions in the active site and keep a −1 charge on cAMP, (2) condition 2: keep two zinc ions in the active site and remove a −1 charge on cAMP, (3) condition 3: remove two zinc ions in the active site and keep a −1 charge on cAMP, and (4) condition 4: remove two zinc ions in the active site and remove a −1 charge on cAMP. For the rigid solutes, condition 2 and 4 are equivalent.

Figure 3 shows cAMP association rates for different ion strengths and reaction radii. All subplots in Figure 3 show that near zero ionic strength, the rates of charged cAMP (condition 1 and 3) binding to PDE are quite low. Although the cAMP active site shows positive potential, the overall charge of PDE is −11. Thus, if cAMP is far from the PDE, it responds to the net negative monopole charge, which generates repulsion forces in the long-range diffusion of the molecules. Thus, it appears that neutral cAMP (condition 2 and 4) binds to PDE faster than the charged one (condition 1 and 3) without electrostatic steering by an ionic atmosphere. The rate constants mostly increase with increasing ionic strength into the physiologically relevant range of 0.05–0.20M. The increase is most dramatic for the most realistic model, condition 1 and reaction radius of 5.44 Å. Indeed, the rate constant increases by orders of magnitude for the charged substrate and physiological ionic strengths upon inclusion of the zinc ion charges [Fig. 3(a)].

Association rate of cAMP to PDE for different reaction radii

The -1 charge on cAMP and the highly positively charged active site of PDE are key factors to create a fast binding process, suggesting that the electrostatic attractions steer the substrate toward to the active site and enhance the association rate of cAMP binding to PDE. Electrostatic steering has been shown to enhance diffusion-controlled rate constants in other enzyme systems.28,29 The PDE case is unusual in that the monopole field of the enzyme is dominated by a large charge of the same sign as that of the substrate. The preferential approach of the charged substrate versus uncharged substrate toward the active site is less pronounced at larger reaction radii, due to the longer range of the repulsive monopole interaction relative to the shorter range of the attractive, higher multipole interactions.

Methods

Molecular systems

The PDE family has 11 classes.30,31 Some are cAMP-selective hydrolases (PDE4, 7 and 8); and some are cGMP-selective (PDE5, 6, and 9). Others can hydrolyse both cAMP and cGMP (PDE1, 2, 3, 10, and 11). PDE 4 and 10 are the two well-studied classes. We chose human PDE4 as a model system. The wild-type PDE crystal structure was taken from Protein Data Bank with the code 3SL3.24 The ligand, a phosphate group, in the cAMP active site was removed to create a ligand-free protein. However, we preserved two zinc ions that bridge the interactions between cAMP and PDE [Fig. 1(a)] because early studies indicated that these zinc ions play a key role on PDE activity and substrate binding.25,26

To model the PDE and create appropriate parameters for electrostatic potential and BD calculations, first, we applied the software Propka version 3.132 to assign static protonation states of the PDE at physiological pH 7.0. Then, charge and radius of each atom in the system were generated by the software PDB2PQR version 1.833 with Amber force field.34 Since the software only contains parameters of standard amino acids, we manually assigned 1.10 Å radius and +2 charges of the two zinc ions based on Stote and Karplus's work.35

Electrostatic potential calculations

The electrostatic properties of the PDE were evaluated by Adaptive Poisson-Boltzmann Solver (APBS) program version 1.4,36,37 which solves Poisson-Boltzmann and related equations to calculate solvation energies and electrostatic potential for analysis and visualization. The input PQR file for the APBS, containing coordinate, radius, and charge of each atom, was generated by the PDB2PQR program.33 We set a specific ionic strength during each electrostatic calculation. Different ionic strengths, 0.00, 0.05, 0.10, 0.15, and 0.20M, were applied in the different calculations. The same setting was also used to generate electrostatic grids for the following BD simulations.

BD simulations

The BD simulations were executed through the Brown Dye package,38 which is able to compute the second order rate constant of the encounter of two rigid bodies moving according to BD. In these simulations, the PDE was constructed as an all-atom model; and cAMP is represented by a single bead with 5.16 Å radius based on the experimental measurement of diffusion coefficient of cAMP.39 The reaction radius, limiting the distance between the center of cAMP and the PDE active site, defines the criteria to terminate the BD simulations. Multiple reaction radii, such as 5.44, 7.00, 9.00, and 11.00 Å [Fig. 1(b)], were used here. Because the probability of successful reactions was low for the smallest reaction radii, a variant of standard BD algorithm, weighted-ensemble method, was turned on to enhance the sampling of diffusion paths.40 To ensure converged results, we performed weighted-ensemble BD simulations in 100,000 steps with 1000 copies of each system to calculate the kon.

Conclusions

In this work, we considered the role of electrostatic steering in the catalytic degradation of cAMP by PDE. We first calculated the electrostatic field around a PDE, and the results indicate that the cAMP active site of the PDE contains highly positive electrostatic potential. We then applied this potential in BD simulations to predict kon of diffusional encounter between PDE and cAMP. The results show that electrostatic attractions between the two molecules guide negatively charged cAMP toward the positively charged active site of PDE, while the steering enhances the rate of the cAMP accurately locating the active site. Although the positive potential around the active site helps to capture diffusing cAMP molecules, the distribution of net negative charges on PDE surface detracts the long-range approach of cAMP from all directions. Thus, proper ionic strength plays a key role in enhancing the association rate.

Acknowledgments

We are grateful to Nuo Wang for helpful discussion about the settings of BrownDye package.

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