Complexity in pH-Dependent Ribozyme Kinetics - ACS Publications

Nov 20, 2017 - We previously published simulations of rate−pH profiles for ribozymes in terms of species plots for the general acid and general base...
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Complexity in pH-Dependent Ribozyme Kinetics: Dark pKa Shifts and Wavy Rate−pH Profiles Erica A. Frankel†,‡ and Philip C. Bevilacqua*,†,‡,§ †

Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, United States Center for RNA Molecular Biology, Pennsylvania State University, University Park, Pennsylvania 16802, United States § Department of Biochemistry and Molecular Biology, Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡

S Supporting Information *

ABSTRACT: Charged bases occur in RNA enzymes, or ribozymes, where they play key roles in catalysis. Cationic bases donate protons and perform electrostatic catalysis, while anionic bases accept protons. We previously published simulations of rate−pH profiles for ribozymes in terms of species plots for the general acid and general base that have been useful for understanding how ribozymes respond to pH. In that study, we did not consider interaction between the general acid and general base or interaction with other species on the RNA. Since that report, diverse small ribozyme classes have been discovered, many of which have charged nucleobases or metal ions in the active site that can either directly interact and participate in catalysis or indirectly interact as “influencers”. Herein, we simulate experimental rate−pH profiles in terms of species plots in which reverse protonated charged nucleobases interact. These analyses uncover two surprising features of pH-dependent enzyme kinetics. (1) Cooperativity between the general acid and general base enhances population of the functional forms of a ribozyme and manifests itself as hidden or “dark” pKa shifts, real pKa shifts that accelerate the reaction but are not readily observed by standard experimental approaches, and (2) influencers favorably shift the pKas of proton-transferring nucleobases and manifest themselves as “wavy” rate−pH profiles. We identify parallels with the protein enzyme literature, including reverse protonation and wavelike behavior, while pointing out that RNA is more prone to reverse protonation. The complexities uncovered, which arise from simple pairwise interactions, should aid deconvolution of complex rate−pH profiles for RNA and protein enzymes and suggest veiled catalytic devices for promoting catalysis that can be tested by experiment and calculation.

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because like dark matter, their influence can be felt but they have not been observed.31 Second, recent evidence points to the pKa of the general acid or base being influenced by other ribozyme constituents, such as nearby cationic nucleobases or metal ions, acting as influencers.24 Such influencers lead to cooperative thermodynamic models with third-order or higherorder dimensionality, which can give “wavy” rate−pH profiles that can be accounted for by global fitting and statistics.24 We were interested in exploring the mechanistic bases behind ribozyme dark pKas and wavy rate−pH plots. We describe herein how the ribozyme partitions between various states, only a subset of which perform catalysis, i.e., are “functional”. Three kinetics schemes are described that build in complexity, incorporating cooperative interactions and then influencers. All three schemes employ what Cleland originally defined in protein enzymes as “reverse protonation”, namely protonation opposite to expectations for the free catalytic residues.32,33 For instance, A, C, and G are found to be catalytic

eneral acid−base catalysis is a pervasive mechanistic strategy in protein and RNA enzymes.1,2 In recent years, an increasing number of small ribozymes3−8 have been reported to use their nucleobases in catalysis, including the hairpin,9 HDV,10 hammerhead,11 glmS,12 twister,13 VS,14 pistol,15 twister sister,16 and hatchet ribozymes.17,18 Mechanistic roles for nucleobases include proton transfer, electrostatic catalysis, and hydrogen bonding with the transition state.19 The four nucleobases have pKa values far from neutrality and so are not optimal for general acid−base catalysis.20 Although the pKa values of some ribozyme bases have been observed experimentally to shift toward neutrality,21−24 much like in protein enzymes, including but not limited to glycosidases,25 cysteine proteinases,26 and alanine racemase,27,28other ribozyme residues either do not give observable shifts or have small apparent shifts.9,14,29 Such pKa shifts can also be apparent and manifest themselves in coupling RNA folding and activity.29,30 This work was motivated by two considerations of nucleobase pKas and catalysis. First, we wondered whether pKas might be shifted toward neutrality and contribute to rate acceleration but be hidden from traditional experimental approaches. We refer to such pKa shifts as “dark” pKa shifts © XXXX American Chemical Society

Received: August 15, 2017 Revised: November 20, 2017

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DOI: 10.1021/acs.biochem.7b00784 Biochemistry XXXX, XXX, XXX−XXX

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Biochemistry in ribozymes in charged states of A+, C+, and G−, respectively, but are expected to be neutral at pH 7 for the free nucleotides. This principle applies to multiple protein enzymes, with more recent examples of a protein arginine deiminase34 and a βlactam synthetase.35 Evidence of reverse protonation in RNA enzymes is manifold: for instance, a cationic general acid of protonated C in the HDV ribozyme is supported by rate−pH profiles,10 inverse thiolate effects,36 Raman crystallography,21 and a crystal structure;37 a cationic general acid of protonated A in the hairpin ribozyme is supported by Raman crystallography;38 while an anionic general base of deprotonated G in the hammerhead and twister ribozymes is supported by rate−pH profiles and a crystal structure.8,11,39 General acid, general base, and influencer species can include not only nucleobases but also the sugar-phosphate backbone, metal ions, and cofactors. For this study, we focus on nucleobase catalysis; however, the same theoretical platform can be readily applied to bimolecular species.24

and base (Figure 1B and Excel simulation in the Supporting Information). This partition function can then be used to calculate the fraction of the functional forms of the general acid ( f HA+), general base ( f B−), and ribozyme [f R(1)] (see the Supporting Information). The fraction of fully functional ribozyme f R(1) dictates the rate−pH profile of ribozyme rate constant kobs, because kobs = f R(1)k1.2 Notably, f R(1) is simply equal to 1/Q. Because HA+ and B− do not interact in this case, the product of the curves for f HA+ (red) and f B− (blue) also gives the fraction of the functional ribozyme (black), as seen mathematically via f HA+ f B− = Q/Q2 = 1/Q = f R(1) and observed graphically (Figure 1C). In other words, the system is additive in free energy. This noncooperative case has a classic “bell-shaped” rate−pH profile (Figure 1C, black trace), which can be attained experimentally if the pKas of the bases are in the experimentally accessible pH range of approximately 5−10.29 In Figure 1C, we consider two scenarios: the pKas of the general acid and general base are 5 and 9, respectively, like in the ground state hairpin ribozyme,9,38 and the pKas of the general acid and general base are shifted toward neutrality at 6 and 8, respectively. As illustrated in Figure 1C, in each case, the fraction of the functional ribozyme is maximal at neutrality when plotted on the logarithmic axis, albeit with a broader maximum for the unshifted pKas. When the pKa values for the general acid and base are farthest from neutrality, at most only one in every 10000 molecules is functional. In contrast, when the general acid and general base pKa values shift one unit closer to neutrality, the effect is logarithmically additive and the functional population increases 100-fold. Additionally, the pKas of the general acid and base are visible: in the logarithmic plot at both the rounding points and extrapolation lines (see the Supporting Information) and in the linear plots at the inflection points. The significant effect that general acid and base pKa values have on the population of f R(1) underscores the importance of pKa shifting to enzyme activity.

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CASE 1. SIMPLE NONCOOPERATIVE MECHANISM The first case is a two-dimensional noncooperative mechanism with two-nucleobase catalysis. This mechanism, which was described by our lab,2 is revisited briefly to frame the influence of cooperative interaction between nucleobases on ribozyme catalysis. In a noncooperative environment where the general acid and base do not interact, the pKa of the general acid remains constant regardless of the protonation state of the general base (top and bottom edges of Figure 1A), and vice versa. This system can be described at any pH using a partition function, Q, that requires only pKa values for the general acid

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CASE 2. COOPERATIVE MECHANISM: EVIDENCE OF DARK pKas We build off of the preceding noncooperative two-nucleobase catalysis and incorporate an attractive, cooperative interaction between the cationic general acid and anionic general base. In this scenario, the corresponding pKas for those species are perturbed along two edges of the scheme (Figure 2A). A similar scenario has also been described using computational methods for protein enzymes, such as in RNase A.40 However, in that case, the general acid and base do not interact and there is no evidence of dark pKas. The pKa of the general acid is unshifted under conditions where the general base is in its neutral, nonfunctional protonated form (top edge of Figure 2A) but shifts upward toward neutrality by ΔpKcoop units, with a coupling free energy of −1.4ΔpKcoop (kcal/mol) under conditions where the general base is in its anionic functional form (bottom edge of Figure 2A).29 Likewise, the pKa of the general base is unshifted under conditions where the general acid is in its neutral nonfunctional deprotonated form (right edge of Figure 2A) but shifts downward toward neutrality by the same ΔpKcoop units under conditions under which the general acid is protonated (left edge of Figure 2A). The population of the functional form of the ribozyme, f R(1), at any pH can again be described using a partition function, although it is now dependent on both the unshifted and shifted pKa values of the general base and general acid (Figure 2B and

Figure 1. Simulations of pH−species plots for noncooperative general acid−base catalysis. (A) Scheme involving a general acid (GA) and general base (GB). (B) Partition function and fractions of GA, GB, and active ribozyme R(1). (C) Species plots of f HA+ with pKas of 5 and 6, f B− with pKas of 9 and 8, and f R(1), on logarithmic (left) and linear axes (right). B

DOI: 10.1021/acs.biochem.7b00784 Biochemistry XXXX, XXX, XXX−XXX

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Biochemistry

Figure 2. Simulations of pH−species plots for cooperative general acid−base catalysis. (A) Scheme involving a general acid (GA) and general base (GB). (B) Partition function and fractions of GA, GB, and active ribozyme R(1). (C) Species plots of f HA+ with pKas for the cooperative case of 5 and 7, f B− with pKas for the cooperative case of 9 and 7, and f R(1) on logarithmic (left) and linear axes (right). pKa values for the noncooperative case are 5 and 9 for the general acid and general base, respectively.

∼7 (Figure 2C left, solid red line), where at the general base starts to significantly populate its deprotonated form (Figure 2C left, solid blue line). At this point, the attraction between f HA+ and f B− is enhanced, leading to a slowing of the rate of deprotonation with pH and a rounding point in the general acid species plot near pH 9, the apparent pKa of the general base. Symmetric processes occur with the general base leading to a rounding point in the general base species plot near pH 5, the apparent pKa of the general acid. The net effect is an increase in the population of f R(1) (Figure 2C left, compare dashed and solid black lines) that is similar to that seen in case 1 wherein the pKas of the general acid and base were 6 and 8, respectively. See Figure S1 for further simulations and discussion of the coupling. Common ways to experimentally measure pKa values include spectroscopic methods such as NMR and Raman, which focus on f HA+ or f B− and typically require a ≥5% population for detection23 and are plotted on linear species plots (Figure 2C, right panel). Although the population of f R(1) is now 100-fold greater at any pH than under a noncooperative scenario, the maximum population of f R(1) still occupies only ∼1% of the total population (Figure 2C, left panel). Indeed, this nonadditive effect is completely hidden when looking at a linear species plot (Figure 2C, right panel). Standard spectroscopic methods are generally not sensitive enough to report these ratepromoting pKa shifts. Furthermore, kinetic methods, which report on f R(1) and are typically plotted on logarithmic species plots (Figure 2C, left panel) would also miss these ratepromoting pKa shifts; i.e., the black trace does not capture the

Excel simulation in the Supporting Information). Under these cooperative conditions, the product of the fraction of the general acid (solid red) and base (solid blue) no longer equals the fraction of the functional ribozyme (solid black). This is shown mathematically in Figure 2B and graphically in Figure 2C. In other words, the system is nonadditive in terms of free energy. In Figure 2C, we again plot the fraction of the functional form of the general acid and general base and the fully functional ribozyme along both logarithmic and linear scales. We consider a single scenario in which the unshifted pKas for the general acid and general base are 5 and 9, respectively, with a ΔpKcoop of 2 units (solid lines), and compare that scenario to the noncooperative case from the previous section (dashed lines). The magnitude of ΔpKcoop of 2 units is based on extrapolation of pKa shifts for model compounds (see the Supporting Information). It is visible from the logarithmic plots that even though the apparent pKa values for the general acid and base measured in an experimental rate-pH profile do not change from 5 and 9 (Figure 2C left, rounding points of the solid black line; or Figure 2C right, inflection points of the solid red and blue lines), consideration of the electrostatic attraction between the two species leads to a nonadditive catalytic effect on the fraction of the functional ribozyme: the population of the functional ribozyme increases by 100-fold versus the noncooperative case. It is insightful to consider the origin of this effect. In the cooperative case, the general acid with an apparent pKa of 5 is deprotonated linearly with increasing pH until the pH reaches C

DOI: 10.1021/acs.biochem.7b00784 Biochemistry XXXX, XXX, XXX−XXX

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Figure 3. Simulations of pH−species plots for cubic cooperative general acid−base catalysis. (A) Scheme involving a general acid (GA), general base (GB), and influencer (I). (B) Partition function and fractions of GA, GB, and active ribozyme R(1) and R(5). (C) Species plots of f HA+ with a fixed pKa of 7, f B− with pKas of 9 and 7, influencer f HI+ (pink) with a pKas of 4 and 6, and f R(1)+R(5), which represents the two fully functional forms of the ribozyme, on logarithmic (top) and linear (bottom) axes. (D) Same as panel C but with a pKa of GA fixed at 11.

profiles, and thus, fractions of functional ribozyme plots are wavy, too. The coupling free energy between HI+ and B− is mathematically and graphically equivalent to that between HA+ and B− in case 2, with a coupling of ΔpKcoop of 2 units. Because the general acid does not couple in the case presented here, coupling between HI+ and B− is the same on the left and right sides of the cube, which is termed direct coupling.43,44 The effect of the influencer makes physical sense in terms of the ribozyme structure. The active sites of ribozymes have nucleobases, which may be charged, in the proximity of the catalytic species.24,45,46 It is thus likely that the ionization states of nucleobases near the active site may affect the ionization state of the general acid and general base. An example of this was recently reported in the hammerhead ribozyme where C17+ interacts with the G12− base24 and has also been seen in oligoalanine models (Table S1).47 Inspection of Figure 3 reveals that there is a near-plateau region for f R(1)+R(5), which represent the two states of the ribozyme with a fully functional general acid and general base, between pH ∼4 and 6 (top graph of Figure 3C). In the case of

wavy data present in the general acid and general base species plots. This leads to the notion that the rate-promoting pKa shifts in Figure 2 are dark pKa shifts and are indecipherable relative to noncooperative models (Figure S2). With this said, recent NMR relaxation−dispersion approaches are allowing users to see rare or “excited” states of RNA, especially where there is a significant chemical shift change between states, as might be expected for altered base protonation states.41,42 Thus, experimental elucidation of these rare pKas in active sites of ribozymes may be on the horizon.

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CASE 3. NUCLEOBASE INFLUENCER: WAVY RATE−pH PROFILES To promote wavy behavior in f R(1), we need an attractive cooperative interaction between an influencer and either a general acid or a general base. In the case provided below, the anionic general base, B−, and cationic influencer, HI+, interact favorably, while for the sake of simplicity, the general acid and general base do not couple. In this way, the population of the general base but not the general acid is wavy in its rate−pH D

DOI: 10.1021/acs.biochem.7b00784 Biochemistry XXXX, XXX, XXX−XXX

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Biochemistry the general acid having a pKa of 7, bell-shaped behavior is observed (Figure 3C top, black line), while in the case of the general acid having a pKa of 11, the high-pH leg of the bell is missing in the experimentally accessible pH range of approximately 5−10 (Figure 3D top, black line). The width of the plateau can be increased by increasing the coupling (ΔpKa) between HI+ and B− (Excel simulations in the Supporting Information). General acid−base catalysis is a ubiquitous catalytic strategy in small ribozymes and protein enzymes alike, utilizing side chains as well as metal ions and cofactors. Depending on the species employed as the general acid and base, the observed rate−pH profiles can take on different shapes. Herein, we explored rate−pH profiles for three cases, motivated by simple pairwise interaction between the anionic general base and cationic general acid, or between the anionic general base and cationic influencer: a noncooperative thermodynamic square, a cooperative thermodynamic square, and a cooperative thermodynamic cube. Relative to the noncooperative case, cooperativity in the thermodynamic square (case 2) leads to rate enhancement without experimentally observable changes in rate−pH profiles for kinetics or signal−pH profiles for spectroscopy. The extent to which such “dark pKas”, which could also include pKas shifted away from neutrality, exist and promote ribozyme or protein enzyme reactivity awaits further exploration. Relative to the noncooperative case, cooperativity in the thermodynamic cube (case 3) leads to “wavy” rate−pH profiles in which the pKa of the functional form of the ribozyme, f R(1) + f R(5), is itself a function of pH. Studies of an enolase protein enzyme also revealed a pH-dependent pKa, with a line shape reminiscent of the black line in Figure 3C top panel, which those authors described as “wavelike”.33 The magnitude of the wave in their study parallels that seen in our study if we set the coupling to one pKa unit. Both this “wavelike” behavior and the “reverse protonation” mentioned above show that similar physical principles apply to enzymes made out of amino acids and nucleotides. A difference is that reverse protonation seems to be the exception in protein enzymes but the rule in RNA enzymes given that the pKas of the free nucleobases are far from neutrality. In case 3, we considered the scenario in which coupling between the influencer and general base is direct, but coupling could also be indirect and depend on the protonation state of the general acid, as well as additional influencers. Such additional complexity could lead to multiple plateaus and the appearance of fractional slopes in rate−pH profiles. Perturbations in the pKas of titratable groups that lead to complexities in the rate profiles such as these have also been supported on a theoretical level for protein enzymes.48−50 Global fitting is an approach that we recently introduced to fit rate−pH profiles that are parametric in Mg2+ concentration that have wavy features.24 Interactions among the general acid, general base, and influencer have been taken herein as electrostatic but could be of other forms that depend on charge state such as cation−π interactions.24,51,52 Calculations and new experimental methods may lend insight into the phenomena described herein.

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Methods, derivations of equations, and supporting figures (PDF) Simulation spreadsheet (XLSX)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (814) 863-3812. ORCID

Philip C. Bevilacqua: 0000-0001-8074-3434 Funding

NASA Exobiology, Grant 80NSSC17K0034. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Jamie Bingaman, Kyle Messina, Drew Veenis, and Scott Showalter for helpful comments.

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ABBREVIATIONS GA, general acid; GB, general base; f HA+, fraction of functional general acid; f B−, fraction of functional general base; f R(1), fraction of functional ribozyme.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.biochem.7b00784. E

DOI: 10.1021/acs.biochem.7b00784 Biochemistry XXXX, XXX, XXX−XXX

Perspective

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DOI: 10.1021/acs.biochem.7b00784 Biochemistry XXXX, XXX, XXX−XXX