How To Draw A Ph Rate Profile

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Biochemistry. Author manuscript; bachelor in PMC 2015 May 23.

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PMCID: PMC4441796

NIHMSID: NIHMS690253

Estimation of pH-action Profiles for Acrid-Base Catalysis from Molecular Simulations

Thakshila Dissanayake

^†Center for Integrative Proteomics Research, BioMaPS Institute and Section of Chemistry & Chemic Biology, Rutgers Academy, 174 Frelinghuysen Road, Piscataway, NJ 08854-8076, United states

Jason Swails

^†Heart for Integrative Proteomics Research, BioMaPS Institute and Section of Chemistry & Chemical Biological science, Rutgers University, 174 Frelinghuysen Road, Piscataway, NJ 08854-8076, USA

Michael E. Harris

^‡Department of Biochemistry, Case Western Reserve University School of Medicine, Cleveland, OH 44106 USA

Adrian E. Roitberg

^¶Breakthrough Theory Project, Chemistry Section, University of Florida, Gainesville, Florida 32611, The states

Darrin Chiliad. York

^†Center for Integrative Proteomics Enquiry, BioMaPS Institute and Section of Chemical science & Chemical Biology, Rutgers University, 174 Frelinghuysen Road, Piscataway, NJ 08854-8076, Usa

Abstract

The measurement of reaction charge per unit as a function of pH provides essential information about mechanism. These rates are sensitive to the pK_a values of amino acids straight involved in catalysis that are ofttimes shifted by the enzyme agile site environs. Experimentally observed pH-rate profiles are usually interpreted using simple kinetic models that allow estimation of "apparent pK_a " values of presumed general acid and base catalysts. 1 of the underlying assumptions in these models is that the protonation states are uncorrelated. In the present work, we innovate the utilize of constant pH molecular dynamics simulations in explicit solvent (CpHMD) with replica commutation in the pH-dimension (pH-REMD) equally a tool to assist in the interpretation of pH-activity data of enzymes, and examination the validity of different kinetic models. Nosotros apply the methods to RNase A, a epitome acid/base catalyst, to predict the macroscopic and microscopic pK_a values, too as the shape of the pH-rate profile. Results for apo and cCMP-bound RNase A hold well with bachelor experimental information, and suggest that deprotonation of the general acrid and protonation of the full general base are non strongly coupled in transphosphorylation and hydrolysis steps. Stronger coupling, all the same, is predicted for the Lys41 and His119 protonation states in apo RNase A, leading to the requirement for a microscopic kinetic model. This type of analysis may be important for other catalytic systems where the active forms of implicated general acid and base are oppositely charged and more highly correlated. These results suggest a new way for CpHMD/pH-REMD simulations to span the gap with experiments to provide a molecular-level interpretation of pH-activity information in studies of enzyme mechanisms.

Acid-base catalysis is a common catalytic strategy in protein and RNA enzymes,^ane and is employed in the cleavage of the RNA phosphodiester backbone by RNase A^two,3 also as small nucleolytic RNA enzymes.^iv Full general base and acrid catalysts facilitate nucleophile activation through proton brainchild, and promote leaving group difference through proton donation, respectively. The observed reaction charge per unit is assumed to be proportional to the probability of finding the enzyme in a "catalytically agile" state with the acid protonated (i.e., able to donate a proton), and the base deprotonated (i.e., able to receive a proton). This conditional probability volition thus be a role of the pH, and the pH-rate curves will be sensitive to the pK_a values of the general acid and base.^five,6

The measurement of reaction kinetics as a function of pH provides vital data about mechanism; notwithstanding, the interpretation of this data is not e'er straightforward.⁶ Experimentally determined pH-rate curves are normally fit to a simple equilibrium model where the credible pThousand_a values of the full general acid and base of operations appear every bit contained parameters. When protonation states are strongly coupled as they frequently are in enzyme active sites, irregular titration beliefs occurs, requiring a more detailed theoretical analysis.^5,seven,8 Recently, computational methods accept emerged that permit molecular simulations in explicit solvent to be performed under abiding pH conditions (CpHMD), and the conditional probabilities of correlated protonation events to be direct determined.^9–sixteen CpHMD can exist used in conjunction with replica exchange molecular dynamics in the pH dimension (pH-REMD) in club to enhance sampling of important states while at the same time providing information over a range of pH values that can exist used to predict complex titration curves.^9,17 The present work reports the starting time application of the CpHMD/pH-REMD method to the prediction of the pH-rate curves for the apo and the 2′,3′-cyclic phosphate (ii′O-transphosphorylation production) bound RNase A, a prototype acrid-base catalyst.

RNase A catalyzes a ii′O-transphosphorylation of a leap RNA substrate that involves cleavage of the phosphodiester backbone to class a 2′,iii′-cyclic phosphate and 5′-hydroxyl termini.^2,iii In a subsequent reaction RNase A catalyzes the hydrolysis of the cyclic phosphate to form a 3′ phosphate. Both transphosphorylation and hydrolysis involve general acid-base catalysis, and thus are strongly pH-dependent. The kinetics of RNase A have been extensively studied,^18,19 including analysis of the roles of His12 and His119^xx and the pH-dependence of substrate association.²¹ In the present work, we examine the upshot of pH on the acid-base of operations catalytic step in RNase A two′O-transphosphorylation and hydrolysis. Nosotros do not consider here the effect of pH on substrate association and bounden, which is known to exist important.²¹ Extension of the theoretical framework to take into business relationship the added dimension of substrate binding is possible, but this requires technical details that are beyond the telescopic of this kickoff application. Even so, we note that very recent progress in this area has been reported.²²

Scheme 1 illustrates the putative mechanism of RNA cleavage via transphosphorylation and hydrolysis of cytidyl-3′-5′adenosine (CpA) and 2′,three′-cyclic phosphate by RNase A.^2,3 The His119/His12 pair is generally accepted general acid/base of operations pair in transphosphorylation (although other mechanisms take been proposed and discussed^three). His12 abstracts the proton from O2′ to facilitate the nucleophilic attack on the adjacent phosphorus cantlet. His119 act as the full general acid to donate a proton to the O5′ leaving group, resulting in a 2′,3′-cyclic phosphate. Subsequent hydrolysis occurs by the action of His119 as the general base to abstract the proton from a water molecule in order to facilitate nucleophilic attack. The His12 residue acts as the general acid to donate a proton to O2′ and leads to the 3′-phosphomonoester final production. Note that some reports in the literature^23,24 have suggested that Lys41, rather than His12, may play the role of the general base in transphosphorylation. Although this machinery is not widely accepted, nosotros nevertheless consider it for comparison.

The putative mechanism of transphosphorylation (left) and hydrolysis (right) past RNase A. The generally accepted view is that H119/H12 acts equally the general acid/base pair in transphosphorylation, and their roles are reversed in hydrolysis. Nonetheless, there has been some debate in the literature that alternatively, K41 might act as full general base in transphosphorylation, although this is less widely accepted.

Methods

Interpretation of pH-rate data for general acid-base catalysis

Scheme 2 illustrates a microscopic kinetic model for full general acid-base catalysis used to interpret pH-activity information. The underlying kinetic assumption is that the catalytic rate is proportional to the active species, AH ⁺Due east _B⁻ , which has the full general base of operations deprotonated (B ⁻) so as to be able to accept a proton and activate the nucleophile, while the general acid (AH ⁺) is protonated so as to be able to donate a proton to the leaving group.

Microscopic full general acid-base protonation state model used to translate pH-activeness data: _{AH ⁺} E _{B ^–} , _{AH ⁺} E _BH , _A Eastward _BH , _A Eastward _{B ^–} are four microstates. E stands for "enzyme" and subscripts A and B indicate the acid and base of operations, respectively. The pG_a shifts discussed in the text are defines every bit Δ p M a , A = p G a , A B H − p K a , A B −, and Δ p Thousand a , B = p Thou a , B A − p Yard a , B A H +. Note the constraint of the thermodynamic cycle ensures ΔpThousand_a,A ,+ΔpYard_a,B =0, and a positive value for ΔpYard_a,B indicates anticooperative coupling of protonation states (i.due east., protonation of the acid site disfavors protonation of the base), whereas a negative value of ΔpK_a,B indicates cooperative coupling (i.e., protonation of the acid site favors protonation of the base). The "apparent pM_a " model discussed in the text involves plumbing equipment of pH-rate data nether the constraint that ΔpK_a,A =−ΔpGrand_a,B =0 (see text). This scheme does not consider the pH-dependence of substrate binding, which is as well important for a complete kinetic label.

The pH-dependent probabilities for each of the four micro-states illustrated in Scheme ii tin can be described by the partition function Q

Q = 1 + 10 p Yard a , B AH + − pH + 10 p G a , B AH + − p 1000 a , A BH + 10 pH − p K a , A B −

(i)

from which the probabilities (fractions) for each country tin be determined equally:

f ( AH + ∕ B ) = ten p Yard a , B AH + − pH ∕ Q

(iii)

f ( A ∕ B ) = x p K a , B AH + − p K a , A BH ∕ Q

(4)

f ( A ∕ B − ) = 10 pH − p M a , A B − ∕ Q

(5)

Note that the reference free energy in the partition function is taken as that of the active country AH ⁺Eastward _B⁻ (gear up to zero energy). The microscopic pG_a values can be determined from fitting to these iv fractions simultaneously under the constraint that their related gratuitous energy values sum to nil in accord with the thermodynamic bicycle shown in Scheme ii. The plots of the data used in deriving microscopic pM_a values can be plant in supporting information.

A common assumption in the interpretation of pH-rate profiles is that the protonation/deprotonation events are uncorrelated; i.e., an equivalence is causeless between microscopic pK_a values p K a , A B H = p G a , A B − and p 1000 a , B A H = p K a , B A, or equivalently that ΔpGrand _a,A = −ΔpThousand _a,B = 0, where Δ p Chiliad a , A = p K a , A B H = p Thousand a , A B − and Δ p Thousand a , B = p K a , B A − p Thousand a , B A H + (for more complete discussion, see reference ⁶). Fitting of the pH-rate data under these constraints leads to apparent pG_a values for the general acid and base of operations, and we volition henceforth refer to this model every bit the "apparent pYard_a model" to distinguish it from the "microscopic pK_a model" which allows this coupling parameter to be optimized. Alternatively, directly determination of the macroscopic pK_a values of the individual acid and base sites involves fitting to each of the corresponding contained acid and base of operations fractions

f _(AH⁺) =f _(AH⁺∕B) +f _{(AH⁺∕B⁻)}

(6)

f _(B⁻ =f _(A∕B⁻) +f _{(AH⁺∕B⁻)}

(7)

using the Hill equation

f _(d) = 1 ∕ one + (10 ^{northward(pK _a−pH)})

(8)

where f _(d) is the deprotonated fraction of the residue of involvement (either f _(AH) or f _(B⁻)) and northward is the Hill coefficient.

Molecular dynamics simulations at constant pH

The starting structures for the simulations were prepared past modifying the crystallographic structure of apo RNase A (PDB ID:1KF5)²⁵ and RNase A complexed with deoxycytidyl-iii′,5′-deoxyadenosine [(d(CpA))] (PDB ID:1RPG)²⁶ solved at 1.xv Å and 1.4 Å resolution, respectively. Two separate sets of explicit solvent constant pH replica exchange molecular dynamics (CpHMD/pH-REMD)^ix simulations were performed using developmental version of Bister 12²⁷ molecular dynamics bundle on apo RNase A and the production state, 2′,3′-cyclic phosphate (cCMP) bound RNase A. The apo and complexed RNase A structures were each placed in a cubic box of TIP4PEw²⁸ water molecules having a buffer of at least 10 Å on each side, and neutralized by chloride counterions for the expected charge of the systems (standard amino acrid protonation states) at pH seven with the exception of His12 and His119 treated every bit fully protonated. Notation that the net number of explicit ions are constant in all the simulations, so the net charge of the organization does vary as titratable residues alter protonation state. This bespeak was addressed specifically with regards to the titration process in Swails et al.⁹ and shown not to affect the titration since the sampling of protonation states occurs using an implicit solvent model based on the conformations generated with explicit solvent simulation. Later on initial minimization and equilibration with molecular dynamics, pH-REMD simulations in explicit solvent^nine were performed at 300K and 1 bar using a total of 24 replicas respective to different pH values between two and 13. During these simulations, His12, Lys41 and His119 were treated equally titratable. Long range electrostatics were computed using the smooth particle-mesh Ewald (PME) method.^29,xxx Annotation that the PME method implicitly introduces a background term that neutralizes the system (sometimes referred to as a "neutralizing plasma") that is further corrected for finite size furnishings³¹ with a volume-dependent term. Other corrections can be made to remove pressure and free energy artifacts for charged periodic systems,³² but in previous studies⁹ these were not found to be necessary and were not used here. Simulations were performed using a 2 fs integration pace, with exchanges between next replicas attempted every 200 fs, and carried out to 74 and 104 ns for each replica of apo and cCMP-bail RNase A. The 60 ns of production simulation was analyzed and reported for both systems. A full description of the simulation protocol, pH-activity curves, convergence tests on the sampled protonation states, and details about the side-chain conformations, hydrogen bonding networks in the active site and bounden of cCMP at different pH values can be found in the supporting information.

Results and Give-and-take

Simulations accurately predict the macroscopic pK_a^s for apo and cCMP-bound RNase A

Analysis of the pH-REMD simulations provides values for the fractions f _(AH⁺ /B⁻), f _(AH⁺ +/BH), f _(A/BH), and f _(A/B⁻ ) described in Eq. (2)-Eq. (5), and hence via Eq. (6) and Eq. (7) the overall acrid and base fractions, f _(AH⁺ ) and f _(B⁻ ). The titration curves for His12, His119 and Lys41 for both apo and cCMP-complexed RNase A can be constitute in Effigy 1. Each fraction is observed to exhibit nigh-ideal Henderson-Hasselbalch beliefs. Fitting the acid and base of operations fractions to the Hill equation (Eq. (8)), allows directly evaluation of the simulated macroscopic pK_a southward. Comparing of the simulated and experimental pM_a values are listed in Table i for both apo and cCMP-complexed RNase A. In the case of apo RNase A, the simulated pK_a values for His12, His119 and Lys41 (5.95, 6.23 and 9.26) are within approximately 0.3 units of the corresponding experimental values.^33,34 The simulations of RNase A complexed with cCMP predict shifted pThou_a values for His12, His119 and Lys41 to 7.95, 7.17 and 9.65, respectively and are in reasonable understanding with the experimentally estimated values 8.0,7.4 and 9.xi, respectively.^34,35 In the course of the simulations over the pH range ii-8, the integrity of the active site is maintained. Beyond pH 8, the interaction betwixt Asp121 and His119 that form the His-Asp catalytic dyad begins to become displaced.³⁶ At loftier pH values, the cCMP becomes more than loosely spring³⁷ in the binding pocket, leading to larger fluctuations and greater difficulty sampling. Details about the key structural features of the simulations at each pH are provided in the supporting information.

Titration curves (lines) fitted to simulation data (points) with the Hill equation [Eq. (8)]. The upper panel represents the apo enzyme and the lower console represents the cCMP-bound enzyme. The Hill coefficients for His119, His12 and Lys41 are 0.94, 0.94, 0.98 for the apo enzyme and i.04, 1.09, 1.10 for the cCMP-bound enzyme, respectively.

Table ane

Comparison of experimental and fake macroscopic pChiliad _as for apo and cCMP-RNase A using the Hill equation and the "apparent pK _a" model.

	His12	His119	Lys41
Apo RNase A
Expt.	5.viii a	6.2 a	ix.0 b
Loma Eq.	five.95 (0.14)	6.23 (0.07)	9.27 (0.07)
Expt. ("Apparent" pKa estimate) c	iv.9-five.two	half-dozen.3-half dozen.9	-
"Apparent" pMa model with H12(B)/H119(A)	5.88 (0.14)	6.27 (0.08)	-
"Credible" pKa model with K41(B)/H119(A)	-	6.17 (0.21)	8.81 (0.21)
cCMP-RNaseA
Expt. (iii′-CMP)	viii.0 d	seven.4 d	ix.11 e
Hill Eq.	7.95 (0.fifteen)	7.17 (0.12)	nine.65 (0.16)
Expt. (cCMP "Apparent" pThoua ) f	8.x	6.xxx	-
Expt. (cCMP "Apparent" pKa ) chiliad	9.0	half dozen.25	-
"Apparent" pKa model with H119(B)/H12(A)	seven.92 (0.16)	seven.16 (0.12)	-
"Apparent" pKa model with H119(B)/K41(A)	-	vii.eighteen (0.xiii)	9.64(0.16)

Simulated protonation states tin be interpreted using a microscopic pK_a model

The microscopic model illustrated in Scheme ii was fit to the simulated fractions of His12 as the general base/acid and His119 as the general acid/base for apo/cCMP-RNase A (Figure 2). The model, which has three independent parameters, fits the simulation data extremely well. This general tendency is that the curves for the cCMP-complex shift to higher pH values relative to those for the apo enzyme. This trend is primarily due to the existence of the negatively charged cyclic phosphate on cCMP that is in adequately close proximity to the titratable residues in the active site. Further, the microscopic pK_a values derived from the fitting are in very good agreement with those measured from NMR experiments³⁶ for the apo enzyme (Table 2). For the cCMP-bound complex, to our knowledge, at that place currently does not exist experimental microscopic pK_a values that would allow a direct comparison. Nonetheless, there are microscopic pM_a values reported for a iii′-UMP inhibitor.³⁶ The microscopic p1000_a values for His12 and His119 in the three′-UMP jump RNase A signal a different tendency than the experimental pOne thousand_a values for 3′-CMP and cCMP- leap RNase A complexes^19,35,38 and the false values reported here (Table 1); nonetheless, we can compare the magnitude of the coupling (ΔpK_a values in Table 2) between protonation states.

Microscopic pK_a model results with H12/H119 acting as the general acrid and base

The plots of the logarithm of protonated fractions, log(f), versus pH of each microstate for apo (elevation) and cCMP-bound RNase A (bottom) were obtained by plumbing fixtures the simulation data for all fractions to the equations derived from the microscopic model (Scheme ii) with His12/His119 acting equally the general base of operations/acid for apo RNase A (transphosphorylation model) and the general acid/base of operations for cCMP-bound RNase A (hydrolysis model), respectively, equally depicted in Scheme 1. The simulation data fits well with RMS errors of 0.22 (apo) and 0.17 (cCMP) for the log(f) values. The log(f) maximums (−0.45 and −0.30) for the curve of the agile fraction, f _{(AH⁺/B^–)}, are at 6.1 (apo) and at seven.v (cCMP), respectively.

Table two

Comparing of experimental and simulated microscopic pThou _asouthward using the microscopic model illustrated in Scheme ii for apo and cCMP-bound RNase A.

	p K a , B A H +	p One thousand a , B A	Δp1000a,B	p Chiliad a , A B H	p 1000 a , A B −	ΔpGranda,A
Apo-RNase A with His12(B )/His119(A)
Expt. a	5.87	vi.xviii	0.31	vi.03	6.34	−0.31
Microscopic model	5.88 (0.14)	half-dozen.05 (0.15)	0.17	6.xiii (0.05)	6.30 (0.x)	−0.17
Apo-RNase A with Lys41(B )/His119(A)
Microscopic model	8.29 (0.xiv)	nine.26 (0.07)	0.97	6.23 (0.07)	7.21 (0.21)	−0.97
cCMP-RNase A with His119(B )/His12(A)
Expt. (iii′-UMP) a	7.95	vii.85	−0.one	6.45	six.35	0.1
Microscopic model	seven.20 (0.12)	6.99 (0.20)	−0.21	eight.12 (0.17)	vii.92 (0.sixteen)	0.21
cCMP-RNase A with His119(B )/Lys41(A)
Microscopic model	7.17 (0.12)	7.41 (0.40)	0.24	nine.40 (0.eighteen)	9.64 (0.16)	−0.24

The experimental microscopic pK_a values propose that the His12 and His119 protonation states are weakly coupled in both the apo enzyme and the three′-UMP bound RNase A (ΔpGrand_a,B values of 0.31 and −0.1 pK_a units, respectively). The calculated microscopic pG_a values are in reasonable agreement, and predict the apo and cCMP-leap RNase A have ΔpK_a,B values of 0.17 and −0.21 pK_a units, respectively. Overall, the experimental and calculated coupling between His12 and His119 protonation states is adequately weak. The observed weak coupling can be explained by the fact that the acid and base protonation sites are adequately far apart in the agile site, and in the catalytically agile state, involve interactions between a neutral and a positively charged residuum (equally opposed to oppositely charged residues). A fairly striking result is that the experimental ΔpK_a,B value for the three′-UMP bound RNase A is negative, suggesting that protonation of one of the active-site histidine residues favors protonation of the other. This observation has been made experimentally³⁶ and has been explained equally a consequence of enhanced interactions with the phosphate when both sites are protonated. The simulation results reported hither are completely consistent with this estimation (see SI for additional details), and as indicated in Tabular array ii, suggest that just in the phosphate-spring systems does such cooperative coupling occur. The fact that the simulation results (both for the apo and cCMP-complex enzymes) tin be precisely fit to all four fractions by the 3-parameter microscopic kinetic model lends acceptance to its validity.

"Apparent" (uncorrelated) pK_a model for His12/His119 is justified for the catalytic steps in RNase A

The experimental analysis of pH-rate data involves plumbing fixtures the observed charge per unit bend to a simple kinetic model with apparent pM_a values for the presumed full general acid and base. The correspondence of directly measured macroscopic pK_a values of presumed full general acid and base residues with the apparent pK_a values is often interpreted as indirect bear witness supportive of their catalytic roles. The computational analog of this procedure would be to fit only the active fraction, f _{(AH⁺/B^–)}, to the thermodynamic cycle shown in Scheme 2, simply with only two free parameters, pK_a,A and pK_a,B (or alternatively, under constraints that p Yard a , A B − = p M a , A B H and p Grand a , B A H + = p K a , B A). The fitted apparent pK_a curve for His12 and His119 equally the general acid and base of operations, respectively, is shown in Figure 3, and the values for the credible pM_a southward are shown in Table 1. Notation that although the credible pK_a values simply consider the active fraction in the fitting, as would be the procedure used to fit experimental curves, these parameters also make up one's mind the fractions of the other protonation states in accord with the sectionalization role in Eq. (1). Unlike experiment, these not-active fractions are bachelor from the simulations, and thus available for comparison. The fit to the agile fraction (red line in Figure three) is splendid; however, model curves for the other fractions, especially f _(A−/BH), are somewhat worse than for the curves shown in Figure ii that involved fitting the microscopic model to all of the fractions simultaneously. Nonetheless, the apparent pOne thousand_a values fitted to the active fraction are in remarkably close agreement (within 0.07 pM_a units) to the macroscopic p1000_a values that were derived from plumbing fixtures the protonation fractions to the Hill equation (Tabular array 1). This is a direct consequence of the very weak coupling between the His12 and His119 protonation states. Nether these weather condition, the assumptions of independent protonation events and the interpretation of the apparent pK_a values used to gain insight into full general acid-base mechanism is a valid i. Note, even so, the nowadays discussion assumes that the only protonation events that are affecting the catalytic activeness are those of the general acid and base, and in many cases this may non be true.

Apparent pK_a model results with H12/H119 interim as the general acrid and base

The plots of the protonated fractions, log(f), versus pH of each microstate for apo (superlative) and cCMP-bound RNase A (lesser) were obtained by fitting the simulation data to Simply the Active FRACTION (f _{(AH⁺/B^–)}, shown in red) with His12/His119 interim as the general base/acid for apo RNase A (transphosphorylation model) and the general acrid/base for cCMP-bound RNase A (hydrolysis model), respectively, every bit depicted in Scheme 1. The model assumes no coupling of the microstates, and although only the agile fraction is considered in the fitting (as would be the example experimentally), the parameters nonetheless are able to determine the other fractions which can be compared with the simulation data. The upper panel represents the apo RNase A and the lower panel represents the cCMP bound RNase A. The RMS errors for the log(f) values are 0.25 (apo) and 0.18 (cCMP) respectively. The log(f) maximums (−0.43 and −0.xxx) for the bend of the agile fraction, f _{(AH⁺/B^–)}, are at 6.ane (apo) and at seven.5 (cCMP), respectively.

Coupling of protonation states for His119 and Lys41 is pregnant

The above example of general acid-base of operations catalysis in apo RNase A, with His12 and His119 as the presumed general acid and base of operations, respectively, indicates that treatment of the protonation states as uncorrelated within the framework of the "apparent pThou_a " model is justified. However, information technology should not exist causeless that this is a full general phenomena. In order to demonstrate this bespeak, we consider the scenario whereby the function of general base is replaced past Lys41 in the kinetic model for the apo RNase A enzyme. Evidence suggests this is likely non the biological role of Lys41 in catalysis past RNase A, but for the purposes of sit-in, it is still instructive to examine.

The microscopic model is able to fit the simulation information very well for all fractions (Figure 4). However, considerably stronger protonation state coupling (ΔpK_a,A =ΔpThousand_a,B =0.97) is observed between Lys41 and His119 relative to that of His12 and His119 (Table ii). The apparent pG_a values for Lys41 and His119 are 8.81 and vi.17, which differ somewhat from the macroscopic pK_a values obtained from the Hill equation (9.27 and six.23, respectively). Moreover, the "apparent pGrand_a model" does non closely reproduce the protonation state fractions (Figure five), including the agile fraction that was used in the plumbing equipment. Although the slopes of the college and lower pH-regimes of the pH-rate curve is not influenced past the interactions between the residues, the maximum probability is observed to be approximately iii times larger. All the same, the predicted pK_a from the microscopic model illustrates that the "apparent pG_a model" has limitations with regard to mechanistic interpretation in the government where central protonation states are more than strongly coupled. This may be especially relevant for some RNA enzymes where the active form of the general acrid and base are oppositely charged species that can be expected to exhibit stronger electrostatic interactions.

Microscopic pK_a model results with K41/H119 acting equally the general acid and base

The plots of the logarithm of protonated fractions, log(f), versus pH of each microstate for apo (top) and cCMP-jump RNase A (bottom) were obtained past fitting the simulation information for all fractions to the equations derived from the microscopic model (Scheme ii) with Lys41/His119 acting every bit the full general base of operations/acrid for apo RNase A (transphosphorylation model) and the general acrid/base for cCMP-bound RNase A (hydrolysis model), respectively. This is not the generally accepted mechanism depicted in Scheme 1, but has all the same received some support in the literature^24,40 and so is considered here for comparison. The RMS errors for the log(f) values are 0.31 (apo) and 0.44 (cCMP) respectively. The log(f) maximums (−2.09 and −0.05) for the curve of the active fraction, f _{(AH⁺/B^–)}, are at 7.7 (apo) and at eight.4 (cCMP), respectively.

Credible pK_a model results with K41/H119 acting equally the general acid and base

The plots of logarithm of protonated fractions, log(f), versus pH of each microstate for apo (elevation) and cCMP-spring RNase A (bottom) were obtained past fitting the simulation data to Merely the Active FRACTION (f _{(AH⁺/B^–)}, shown in crimson) with Lys41/His119 interim every bit the general base/acid for apo RNase A (transphosphorylation model) and the general acid/base for cCMP-leap RNase A (hydrolysis model), respectively. This is not the generally accustomed mechanism depicted in Scheme 1, merely has nonetheless received some support in the literature^24,40 and so is considered here for comparison. The model assumes no coupling of the microstates, and although only the active fraction is considered in the fitting (as would exist the case experimentally), the parameters nonetheless are able to make up one's mind the other fractions which tin exist compared with the simulation data. The upper console represents the apo RNase A and the lower panel represents the cCMP jump RNase A. The RMS errors for the log(f) values are 0.33 (apo) and 0.48 (cCMP) respectively. The log(f) maximums (−2.69 and −0.xi) for the curve of the agile fraction, f _{(AH⁺/B^–)}, are at vii.v (apo) and at 8.4 (cCMP), respectively.

Summary and Perspective

Recently, advances in computational methods take allowed simulations of biological molecules to be performed in explicit solvent nether abiding pH atmospheric condition. These simulations let conformations and protonation states to be sampled together beyond a range of pH conditions. This enables the prediction of pH-rate curves from molecular simulation, besides equally tools to provide atomic-level estimation of pH-activity data. More importantly, this method allows one to quantify the probability of finding an enzyme arrangement in a catalytically agile protonation state from which it is capable to proceed to react with a pseudo beginning-order rate abiding in the catalytic chemical step. Together with other methods, such as combined breakthrough mechanical/molecular mechanical simulations that tin exist used to map the free energy landscape for the catalytic chemical steps of the reaction, a complete description of catalysis can exist obtained and compared directly with experimental data. The results described here demonstrate promise for theory and experiment to work together to empathise enzyme mechanisms.

Supplementary Material

Supplemental

Acknowledgments

Special thanks to Timothy Giese, Ming Huang and Maria Panteva for their for useful suggestions on the manuscript.

Funding

This work was financially supported past the National Institute of Health (NIH) grant number GM062248 to D.K.Y., NIH grant GM096000 to M.Eastward.H. and National Science Foundation (NSF) grant numbers ACI-1147910 and ACI-1036208 to A.E.R. The simulations were carried out with the Blueish Waters supercomputer, supported by the NSF grant numbers ACI-0725070 and ACI-1238993, and the Extreme Scientific discipline and Engineering science Discovery Environment (XSEDE), supported by NSF grant number OCI-1053575.

Footnotes

Supporting Data Available

A full clarification of the simulation protocol, pH-activity curves, convergence tests on the sampled protonation states, and details most the side-chain conformations, hydrogen bonding networks in the active site and binding of cCMP at different pH values tin can be found in the supporting information. This material is available complimentary of charge via the Internet at http://pubs.acs.org/.

References

1. Kirby AJ. Encyclopedia of Life Sciences (ELS) John Wiley & Sons, Ltd; Chichester: 2010. Affiliate Acid-Base of operations Catalayis past Enzymes. [Google Scholar]

2. Raines RT. Ribonuclease A. Chem. Rev. 1998;98:1045–1065. [PubMed] [Google Scholar]

3. Cuchillo CM, Nogués MV, Raines RT. Bovine pancreatic ribonuclease: Fifty years of the first enzymatic reaction mechanism. Biochemistry. 2011;50:7835–7841. [PMC free commodity] [PubMed] [Google Scholar]

iv. Doudna JA, Cech TR. The chemical repertoire of natural ribozymes. Nature. 2002;418:222–228. [PubMed] [Google Scholar]

v. Onufriev A, Instance DA, Ullmann GM. A novel view of pH titration in biomolecules. Biochemistry. 2001;40:3413–3419. [PubMed] [Google Scholar]

6. Bevilacqua PC. Mechanistic considerations for full general acid-base catalysis past RNA: Revisiting the machinery of the hairpin ribozyme. Biochemistry. 2003;42:2259–2265. [PubMed] [Google Scholar]

7. Ullmann GM. Relations between protonation constants and titration curves in polyprotic acids: A critical view. J. Phys. Chem. B. 2003;107:1263–1271. [Google Scholar]

viii. Klingen AR, Bombarda Due east, Ullmann GM. Theoretical investigation of the beliefs of titratable groups in proteins. Photochem. Photobiol. Sci. 2006;5:588–596. [PubMed] [Google Scholar]

9. Swails JM, York DM, Roitberg AE. Abiding pH replica exchange molecular dynamics in explicit solvent using discrete protonation states: Implementation, testing, and validation. J. Chem. Theory Comput. 2014;ten:1341–1352. [PMC gratuitous article] [PubMed] [Google Scholar]

10. Wallace JA, Shen JK. Continuous constant pH molecular dynamics in explicit solvent with pH-based replica exchange. J. Chem. Theory Comput. 2011;vii:2617–2629. [PMC gratuitous commodity] [PubMed] [Google Scholar]

xi. Wallace JA, Shen JK. Charge-leveling and proper handling of long-range electrostatics in all-atom molecular dynamics at constant pH. J. Chem. Phys. 2012;137:184105. [PMC free article] [PubMed] [Google Scholar]

12. Goh GB, Knight JL, Brooks CL. Constant pH molecular dynamics simulations of nucleic acids in explicit solvent. J. Chem. Theory Comput. 2012;8:36–46. [PMC free article] [PubMed] [Google Scholar]

thirteen. Goh GB, Knight JL, III CLB. pH-dependent dynamics of complex RNA macromolecules. J. Chem. Theory Comput. 2013;9:935–943. [PMC costless commodity] [PubMed] [Google Scholar]

14. Baptista AM, Teixeira VH, Soares CM. Constant-pH molecular dynamics using stochastic titration. J. Chem. Phys. 2002;117:4184–4200. [Google Scholar]

fifteen. Donnini S, Tegeler F, Groenhof One thousand, Grubmüller H. Abiding pH molecular dynamics in explicit solvent with λ-dynamics. J. Chem. Theory Comput. 2011;vii:1962–1978. [PMC costless article] [PubMed] [Google Scholar]

16. Börjesson U, Hünenberger PH. Explicit-solvent molecular dynamics simulation at abiding pH: Methodology and awarding to modest amines. J. Chem. Phys. 2001;114:9706–9719. [Google Scholar]

17. Itoh SG, Damjanović A, Brooks BR. pH replica-substitution method based on detached protonation states. Proteins. 2011;79:3420–3436. [PMC free article] [PubMed] [Google Scholar]

18. Findlay D, Mathias AP, Rabin BR. The active site and machinery of action of bovine pancreatic ribonuclease. 4. The action in inert organic solvents and alcohols. Biochem. J. 1962;85:134–138. [PMC free article] [PubMed] [Google Scholar]

19. Eftink MR, Biltonen RL. Energetics of ribonuclease A catalysis. 1. pH, ionic force, and solvent isotope dependence of the hydrolysis of cytidine cyclic 2′,three′-phosphate. Biochemistry. 1983;22:5123–5134. [PubMed] [Google Scholar]

20. Park C, Schultz LW, Raines RT. Contribution of the active site histidine residues of ribonuclease A to nucleic acid binding. Biochemistry. 2001;40:4949–4956. [PubMed] [Google Scholar]

21. Park C, Raines RT. Catalysis by ribonuclease A is limited past the rate of substrate association. Biochemistry. 2003;42:3509–3518. [PubMed] [Google Scholar]

22. Kim MO, Blachly PG, Kaus JW, McCammon JA. Protocols utilizing constant pH molecular dynamics to compute pH-dependent binding free energies. J Phys Chem B. 2014 DOI:10.1021/jp505777n. [PMC free article] [PubMed] [Google Scholar]

23. Wladkowski BD, Krauss Chiliad, Stevens WJ. Ribonuclease A catalyzed transphosphorylation: An ab Initio theoretical study. J. Phys. Chem. 1995;99:6273–6276. [Google Scholar]

24. Wladkowski BD, Ostazeski P, Chenoweth S, Broadwater SJ, Krauss G. Hydrolysis of cyclic phosphates by ribonuclease A: A computational study using a simplified ab initio quantum model. J. Comput. Chem. 2003;24:1803–1811. [PubMed] [Google Scholar]

25. Berisio R, Sica F, Lamzin VS, Wilson KS, Zagari A, Mazzarella L. Atomic resolution structures of ribonuclease A at six pH values. Acta Crystallogr. D. 2002;58:441–450. [PubMed] [Google Scholar]

26. Zegers I, Maes D, Dao-Thi M-H, Poortmans F, Palmer R, Wyns L. The structures of RNase A complexed with iii'-CMP and d(CpA): Active site conformation and conserved water molecules. Protein Sci. 1994;3:2322–2339. [PMC free article] [PubMed] [Google Scholar]

27. Case DA, et al. Amber 12. Academy of California, San Francisco; San Francisco, CA: 2012. [Google Scholar]

28. Horn HW, Swope WC, Pitera JW, Madura JD, Dick TJ, Hura GL, Caput-Gordon T. Development of an improved 4-site water model for biomolecular simulations: TIP4P-Ew. J. Chem. Phys. 2004;120:9665–9678. [PubMed] [Google Scholar]

29. Darden T, York D, Pedersen L. Particle mesh Ewald: An North log(N) method for Ewald sums in large systems. J. Chem. Phys. 1993;98:10089–10092. [Google Scholar]

30. Essmann U, Perera 50, Berkowitz ML, Darden T, Hsing L, Pedersen LG. A smooth particle mesh Ewald method. J. Chem. Phys. 1995;103:8577–8593. [Google Scholar]

31. Figueirido F, Del Buono GS, Levy RM. On finite-size effects in estimator simulations using the Ewald potential. J. Chem. Phys. 1995;103:6133–6142. [Google Scholar]

32. Bogusz Southward, Cheatham TE, III, Brooks BR. Removal of force per unit area and free energy artifacts in charged periodic systems via net charge corrections to the Ewald potential. J. Chem. Phys. 1998;108:7070–7084. [Google Scholar]

33. Markley JL. Correlation proton magnetic resonance studies at 250 MHz of bovine pancreatic ribonuclease. I. Reinvestigation of the histidine meridian assignments. Biochemistry. 1975;14:3546–3554. [PubMed] [Google Scholar]

34. Jentoft J, Gerken T, Jentoft N, Dearborn D. [¹³C]Methylated Ribonuclease A, ¹³C NMR studies of the interaction of lysine 41 with active site ligands. J. Biol. Chem. 1981;256:231–236. [PubMed] [Google Scholar]

35. Meadows DH, Jardetzky O. Nuclear magnetic resonance studies of the construction and bounden sites of enzymes. Iv. Cytidine 3'-monophosphate binding to ribonuclease. Proc. Natl. Acad. Sci. USA. 1968;13:406–413. [PMC free article] [PubMed] [Google Scholar]

36. Quirk DJ, Raines RT. His . . . Asp catalytic dyad of ribonuclease A: Histidine pKa values in the wild-type, D121N, and D121A enzymes. Biophys. J. 1999;76:1571–1579. [PMC gratuitous commodity] [PubMed] [Google Scholar]

37. Neuberger A, Brocklehurst Grand, editors. Hydrolytic Enzymes; New Comprehensive Biochemistry. Elsevier; Amsterdam, The Netherlands: 1987. [Google Scholar]

38. Herries D, Mathias AP, Rabin BR. The active site and machinery of activeness of bovine pancreatic ribonuclease. 3. The pH-dependence of the kinetic parameters for the hydrolysis of cytidine 2′,3′-phosphate. Biochem.J. 1962;85:127–134. [PMC gratuitous article] [PubMed] [Google Scholar]

39. Gu H, Zhang S, Wong K-Y, Radak BK, Dissanayake T, Kellerman DL, Dai Q, Miyagi M, Anderson VE, York DM, Piccirilli JA, Harris ME. Experimental and computational analysis of the transition state for ribonuclease A-catalyzed RNA 2'-O-transphosphorylation. Proc. Natl. Acad. Sci. USA. 2013;110:13002–13007. [PMC free article] [PubMed] [Google Scholar]

40. Wladkowski BD, Krauss M, Stevens WJ. Transphosphorylation catalyzed by ribonuclease A: Computational study using ab Initio constructive fragment potentials. J. Am. Chem. Soc. 1995;117:10537–10545. [Google Scholar]

Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4441796/

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