Linking protein dynamics to enzyme catalysis

Ioanna Zoi, Dimitri Antoniou, Steven D. Schwartz∗

Department of Biochemistry, University of Arizona, Tucson, AZ 85721, USA

Abstract

Methods that have shown promise for the study of possible coupling of fast pro-tein motions to the enzymatic barrier crossing event are transition path sampling(computationally) and Born-Oppenheimer enzymes (experimentally). We presentcombined theoretical and experimental studies in which we created a mutant en-zyme of purine nucleoside phosphorylase whose rate of chemistry is faster thanthe native enzyme.

Keywords: Born-Oppenheimer enzymes, inverse isotope effects, PNP, TransitionPath Sampling, rate promoting vibrations

1. Introduction1

The role of protein motions in catalysis remains a topic of debates. There is2

a suggestion that dynamics does not contribute to the catalytic efficiency, which3

is said to be mostly due to electrostatic preorganization [1]. Others suggest that4

this is a semantic, rather than substantial distinction [2]. It is useful to recall that5

the catalytic turnover consists of several stages, binding of the substrate, chemi-6

cal turnover, product release, each with its own requirements. In some enzymes7

(e.g. DHFR) certain conformational motions have been identified as necessary8

for preparing the system for reaction [3–6]. This is undoubtedly a case where dy-9

namics is related to catalysis, but in this review we will focus our attention to a10

different type of dynamics. Conformational motions are slow dynamical motions,11

and the chemical barrier crossing, which happens typically within 10-50 fs, takes12

∗Corresponding authorEmail addresses: ioannazoi@email.arizona.edu (Ioanna Zoi),

antoniou@email.arizona.edu (Dimitri Antoniou), sschwartz@email.arizona.edu(Steven D. Schwartz)

Preprint submitted to Comprehensive Natural Products III: Chemistry and Biology.October 15, 2019

place at a frozen instance of these motions. On the other hand, we are interested in13

fast sub-ps motions, of the same timescale as transition state (TS) crossing, when14

these motions and the barrier crossing are kinetically coupled. Some authors con-15

flate both slow and fast protein motions in their discussion of their relevance to16

enzymatic rates, even though the different contributions of such motions in rates17

is known in biochemistry since the classic work on CO rebinding to heme pro-18

teins [7].19

Our group has studied and identified such fast motions in certain enzymes20

[8–10], like lactate dehydrogenase and purine nucleoside phosphorylase (PNP),21

while in another case we did not find fast dynamics to be part of the reaction22

coordinate [11]. Our computational work has been done in collaboration with23

the Schramm experimental group, and the simulations and experiments generate a24

coherent picture of the role of dynamics in TS crossing [12]. Other experimental25

groups have also reported cases where fast dynamics is part of catalysis [13–17].26

Our computational analysis is based on Transition Path Sampling (TPS), which27

will we review in the next Section. It is a Monte Carlo method that generates re-28

active trajectories without prior assumptions about the reaction coordinate. Since29

these trajectories are a few hundred fs long, this method provides information30

about the chemical barrier crossing event only. After an ensemble of reactive tra-31

jectories has been generated, analysis identifies residues and atoms participating32

in the reaction coordinate. The most important benefit of TPS is that one can33

identify at the atomistic level the necessary motions for TS crossing. In fact, the34

effect of these rate promoting fast motions can be understood as an electrostatic35

preorganization effect in a dynamical sense: fast protein motions create electro-36

statically important structures, which have short duration (see the Summary in37

Section 5 and Ref. [18]). Recalling the discussion in the opening paragraph about38

the catalytic efficiency of enzymes, our concern in this review is methods to iden-39

tify which residues are important for TS crossing, and how we can manipulate and40

mutate residues to obtain desirable outcomes.41

Experimentally it is difficult to directly probe motions at the fs timescale that42

is our focus. Recently, our experimental collaborator introduced [19] a method for43

testing the effect of dynamics on chemical catalysis, the use of Born-Oppenheimer44

or “heavy” enzymes, where all 12C, 14N and nonexchangeable hydrogens are re-45

placed by heavier isotopes. The original idea of the Born-Oppenheimer or heavy46

enzyme was to affect the frequency of fast atomic motions in the enzymatic sys-47

tem without affecting the potential energy surface that controls chemistry. The48

heavy enzyme was termed a “Born-Oppenheimer enzyme” because, while the49

heavier atomic masses change bond vibrational frequencies and hence collective50

2

protein motions, they have no effect on the electronic potential energy surface that51

governs the chemical step. Since all H-bonds from exchangeable groups at the52

catalytic site are normal, the only heavy mass effect is from nonexchanged atoms53

with altered vibrational modes throughout the entire enzyme. Traditional kinetic54

isotope effects (KIE) based on reactant isotope labels provide static information55

about the structure of the transition state. However, the KIE in the heavy enzyme56

case provides information on the involvement of protein motions in chemistry.57

There have already been surprising results, e.g. inverse KIEs where the chemical58

step is slower in the native enzyme [20, 21]. Current studies by us and others,59

test the role of individual residues by labeling specific residues. Heavy enzyme60

studies are a developing field and there are already reviews of the heavy enzyme61

literature [22, 23].62

This review will describe results on the native and heavy PNP, and mutations63

we have designed that affect the chemical step. The structure of the review is as64

follows. The next Section provides the background information needed for the65

design studies: we will present results on native PNP and identify the fast motion66

that triggers a sequence of events that lead to barrier crossing; we will describe67

results on heavy PNP and show that there is a crucial mistiming of the motion we68

identified in the native enzyme; finally we will briefly describe Transition Path69

Sampling, which is the main computational and analysis tool we use. Then in70

Section 3 we will describe the first design attempt, that fixed the mistiming of71

motions in the heavy enzyme, but introduced another defect. In Section 4 a sec-72

ond design attempt corrects the defect that was introduced in the previous Section.73

Finally, in Section 5 a third design attempt led to a heavy enzyme whose rate of74

chemistry was faster than the native enzyme. Probably the most important mes-75

sage is that the combination of TPS and the heavy enzyme methodology allowed a76

logical progression for selecting the mutations of the design attempts that reached77

the desired outcome.78

2. Case Study: Human Purine Phosphorylase (hPNP)79

Human PNP is a homotrimer that catalyzes the reversible phosphorolysis of80

the N-ribosidic bond of purine nucleosides and deoxynucleosides [24]. The active81

site of PNP is shown in Figure 1. The glycosidic bond cleavage N9–C1′ occurs82

before the formation of the bond OP–C1′ to the phosphate group.83

We have studied PNP extensively, computationally and in collaboration with84

the Schramm group who have studied it experimentally, as a system where fast85

protein motions are involved in the catalytic step and also as a model system86

3

Figure 1: Substrate guanosine and important active site residues in PNP.

where study of the heavy enzyme supports the atomistic details of these motions87

predicted by computation. From this earlier work we will briefly summarize two88

results that are relevant for the design studies that are the focus of this review.89

2.1. Fast protein motions90

Computational and experimental studies of PNP by our group and by collab-91

orators [10, 25, 26] showed that a His257-initiated compression of O5′ towards92

the O4′ of the purine ring is crucial for TS formation: His257 is hydrogen-bonded93

(ND1 to O5′ of the substrate) to the ribosyl 5′-hydroxyl group and directs O5′ to-94

ward the O4′ of the purine ring, thus destabilizing the ribosidic bond to facilitate95

departure of the purine leaving group. Loss of the N-ribosidic bond causes C1′96

migration toward an anionic oxygen of the phosphate to complete product forma-97

tion. This His257-initiated compression is an example of a fast rate-promoting98

enzyme vibration.99

Using Transition Path Sampling we computationally identified residues that100

are part of the reaction coordinate and analyzed their role in the catalytic mech-101

anism [27]. We confirmed that residues Asn243, Ser220, Glu201, Ser33, Tyr88,102

His86, and His257 are part of the reaction coordinate for native PNP. Interac-103

tions that facilitate approach to the transition state involve activation of the leaving104

group (Asn243 and Glu201), formation of the ribocation (His257 and Tyr88) and105

activation of the phosphate nucleophile (Ser33, His86 and Ser220).106

The most important characteristic found in the reactive trajectories harvested107

by TPS is that in native PNP the compression of the O5′–O4′ distance is coordi-108

nated with TS barrier crossing, as shown in Figure 2. This coordination was used109

as a target for the designed mutants.110

4

0 100 200 300 400 5002.0

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ista

nce (

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Figure 2: Representative trajectories showing the O5′–O4′ compression with respect to the TSlocation for: Native PNP, Heavy PNP, “Mixed” PNP (defined below), Mutant and Mutant HeavyPNP (defined in the next Section). The vertical dashed line (red) shows the location of the TS. Notethe coordination of O5′–O4′ oxygen compression with TS crossing in Native, which is absent inNative Heavy. This coordination is recovered in the mixed enzyme.

2.2. Heavy PNP111

Heavy hPNP is expressed with the nonexchangeable H, C and N isotopically112

substituted to 2H, 13C and 15N. The steady state kinetics parameters kcat and KM did113

not change in the heavy enzyme, consistent with long-timescale protein motions,114

such as reactant binding and product dissociation, being the same as in the native115

enzyme. Critically, the transition state structure (deduced from intrinsic kinetic116

isotope effects) did not change in the heavy enzyme.117

However, the on-enzyme chemical step, measured by single-turnover rate con-118

stants for bound reagents [19], is slower by 30% for heavy PNP. Since in a Born-119

Oppenheimer enzyme the electrostatics is the same but bond vibrational frequen-120

cies are different, evidently in the heavy enzyme the coupling of enzymatic bond121

vibrations to transition state barrier crossing has changed.122

We have identified computationally [28] this change: the important oxygen123

compression initiated by His257 is different in the native and heavy enzymes,124

in particular the compression of the O5′–O4′ distance that was coordinated with125

barrier crossing in the native PNP, is mistimed in the heavy enzyme, where the126

maximum compression happens well after TS crossing (Figure 2). Restoring this127

coordination was a central goal of the mutations we will describe later in the text.128

5

2.3. Rate-promoting motions: local or global protein motions?129

We saw that the native and heavy PNP show differences in the TS crossing130

event, that are associated with a compression of the oxygens, This compression131

may originate either in local motions of residues in the vicinity of the active site132

of the enzyme, or in global changes of its protein structure. To find which of133

these alternatives explains the observed difference, we computationally mutated134

the heavy enzyme by mutating the seven residues that are part of the reaction-135

coordinate into lighter isotopes, while the rest of the enzyme remained isotopically136

labeled (this enzyme we call “mixed” in Figure 2) [27].137

In this “mixed” enzyme the O5′–O4′ compression and its timing with respect138

to TS formation are similar to the native PNP. We also found that the “ mixed139

” enzyme has the same reaction coordinate as the native PNP. This implies that140

the catalytic defect of the heavy enzyme has its origin in the mass-sensitive mo-141

tion of the active site residues. Experimental KIE work [29] has confirmed the142

computational prediction that heavy PNP effects are local to the catalytic site.143

2.4. Transition Path Sampling144

The computational tool we have used is Transition path sampling (TPS) [30–145

32] Our group has pioneered the use of TPS in the study of enzymatic reactions146

[10, 33–37], and recently in enzyme design [27, 38, 39].147

TPS performs a Monte Carlo search in the trajectory space that generates an148

ensemble of reactive trajectories. Because of the ergodicity of classical dynamics149

the generated reactive trajectories quickly decorrelate. Unlike other methods, TPS150

does not require a priori knowledge of a reaction coordinate. Rather, post hoc151

analysis of the generated reactive trajectory ensemble can lead to identification of152

the reaction coordinate.153

This post-simulation analysis is performed in two stages. The first, called the154

committor analysis [40], locates the transition state in each reactive trajectory,155

defined as the time slice with the property that new trajectories initiated from that156

slice with random momenta have probability 0.5 to reach reactants or products,157

in other words, it has an isocommitting property. The set of these isocommittor158

structures form the transition state ensemble (TSE), also called the “separatrix”.159

Once a TS ensemble has been obtained from the harvested reactive trajec-160

tories, one proceeds to the second stage of the analysis, the reaction coordinate161

identification. In the TPS worldview the TS is defined dynamically by the iso-162

committing property. To identify the reaction coordinate one starts from a struc-163

ture belonging to the TS ensemble and makes a guess for coordinates that are part164

6

of the reaction coordinate. Then, one performs a constrained simulation: the de-165

grees of freedom tested for the reaction coordinate are restrained, while the rest166

of the protein is allowed to evolve without restraints. If the guess for the reaction167

coordinate were correct, structures along the constrained trajectory will preserve168

the isocommitting property of the initial structure (which was a TS). If this is not169

the case, one makes another guess for the reaction coordinate and repeats this170

procedure.171

3. PNP design I: Correction of the mistiming of the oxygen compression172

3.1. Design Rationale173

We saw in Section 2.2 that in heavy PNP there was a mistiming of the oxygen174

compression with respect to TS crossing and a decrease of the chemical step rate.175

The aim of the first design study was to identify mutations for heavy PNP that176

would reverse these defects.177

Recall that the oxygen compression is initiated by a motion of His257. RMSF178

calculations showed that His257 is less mobile in the heavy than in the native en-179

zyme. To restore its flexibility, we mutated [27] two second layer residues that lie180

on the distal side of His257 with respect to the catalytic site geometry (Figure 3).181

Conversion of Glu258 to Asp and Leu261 to Ala increased the dynamic access of182

His257, in its distal side with respect to the active site. These mutations did not183

alter the primary contacts between the enzyme and reactants found by crystallo-184

graphic analysis [27].185

3.2. Computational analysis186

In silico mutation of both the native and heavy enzymes (we denote them as187

“light mutant” and “heavy mutant” respectively), was followed by a TPS analy-188

sis. Since these mutations are conservative ones, not altering charges, there are no189

changes in electrostatic effects. Our TPS simulations suggest that in heavy mutant190

PNP, the mutations restore the coordination of the dynamics of O5′–O4′ compres-191

sion with TS crossing, to be similar to that of native PNP (Figure 2 and Table 1).192

Furthermore, committor distribution analysis showed that these mutations do not193

affect the composition of the reaction coordinate of the native PNP.194

Even though the mistiming was corrected, Table 2 shows that in the mutant195

heavy PNP the minimum distance (maximum compression) of the O5′–O4′ dis-196

tance, before the TS and at the moment of TS crossing, has a larger value than197

in native PNP. Recall that the heavy enzyme, even though it had the compression198

7

Figure 3: Structures after the chemical event, showing the active site and reaction coordinateresidues in heavy (left) and heavy mutant (right). In yellow we depict the mutated residues.Residue Glu258 was mutated to Asp and Leu261 to Ala.

mistimed, achieved a compression of O5′–O4′ similar to the native PNP. This de-199

creased promoting interaction is identified as the reason for the slowed chemistry200

observed compared to the heavy PNP, that we discuss next.201

3.3. Effects on kinetics202

Both computer simulations and experimental TS analysis did not detect any203

significant differences between the structures of the native and the two mutant204

enzymes. Although computational results for the light mutant and heavy mutant205

PNPs showed that the mutations restored the dynamics of O5′–O4′ compression,206

the rate of transition state crossing was decreased by two orders of magnitude,207

showing that the Glu258Asp and Leu261Ala mutations resulted in uncoupling of208

the femtosecond motions between catalytic site groups and reactants [29].209

The enzymatic kinetic parameters for the light, heavy and mutant enzymes210

are given in Table 3. Steady-state kinetics are reflected on kcat and pre-steady-211

state kinetics on kchem. In PNPs product release is slow and thus it is the rate-212

limiting step resulting in similar steady-state kinetics, so single-turnover kinetics213

is measured by kchem.214

8

O5′–O4′ time (fs) separatingminimum distance (Å) minimum distance from TS

WTL 2.53 ± 0.06 −17 to +3WTH 2.62 ± 0.10 +36 to +68MutL 2.71 ± 0.08 −16 to +14MutH 2.76 ± 0.04 −16 to +17

Table 1: Minimal values of the O5′–O4′ distance averaged over all trajectories, and range of timeseparation of that minimum from the TS crossing.

O5′–O4′ distance (Å) O5′–O4′ distance (Å)10 fs before the TS at the TS

WTL 2.57 ± 0.04 2.56 ± 0.07WTH 2.93 ± 0.05 2.94 ± 0.06MutL 2.81 ± 0.06 2.78 ± 0.08MutH 2.81 ± 0.07 2.82 ± 0.06

Table 2: O5′–O4′ distances during the TS crossing.

The mutants restored one aspect of dynamics (timing of the compression) but215

lost the coupling of His257 motion towards TS formation, and this loss resulted216

in a decrease of the chemical rate. A more positive way to view this result is that217

once the rate promoting vibration effect was “turned off” by the mutations, there218

was no difference between the light and heavy enzymes.219

These results provided atomistic information into the catalytic event and pro-220

vided insights for a second attempt in design, which we discuss in the next Section.221

kcat (s−1) KM(µM) kcat/KM (M−1 s−1 ) kchem (s−1) on-enzyme KIE

WTL 8.8 ± 0.5 63 ± 8 (1.4 ± 0.2) × 105 157 ± 6.04WTH 8.0 ± 0.3 54 ± 4 (1.5± 0.1) × 105 130 ± 3.4 1.21 ± 0.06MutL 4.2 ± 0.4 73 ± 13 (5.8 ± 1.1) × 104 1.57 ± 0.01MutH 4.2 ± 0.2 64 ± 9 (6.6 ± 1.0) × 104 1.58 ± 0.01 0.997 ± 0.005

Table 3: Kinetic constants for native and mutant PNPs.

9

4. PNP design II: Inverse isotope effects222

We have seen that in the native enzyme the O5′–O4′ compression is strongly223

correlated to the catalytic chemistry rate. In the previous Section we described224

mutations that restored the timing of the oxygen compression relative to transition225

state crossing, but this compression was smaller than in the native enzyme and226

the rate promoting became uncoupled from TS crossing. In this Section we will227

describe work that identified mutations that reversed this uncoupling [38].228

4.1. Enzyme Design Strategy229

We computationally screened mutations near the catalytic site, monitoring the230

O4′–O5′ distance. We examined the geometries of the active sites of the native and231

heavy enzymes, and the dynamics from the reactive trajectories generated in the232

earlier work [27], trying to identify a residue close to His257 with an orientation233

that would favor either compression of the His257-O5′–O4′ axis of oxygen atoms234

(the promoting motion), or directly influence the motion of O5′.235

A good candidate residue for mutation was Phe159, belonging to a hydropho-236

bic group in the adjacent monomer, immediately conterminous to the ribosyl moi-237

ety. Phe159 is not a highly conserved amino acid among PNPs, and while its side238

chain is pointing toward the active site it is not in van der Waals contact with the239

reactants. The orientation of the aromatic ring is parallel to the His257 ring and is240

close to the atom ND1 of His257, therefore it is in a favorable position to influence241

the motion of the His257-O5′–O4′ promoting motion (Figure 4), which made it242

an ideal candidate for mutation. We mutated computationally Phe159 to Tyrosine243

(F159Y), which added a hydroxyl group, with the expectation of an increase in244

optimizing interactions toward the TS. We performed this mutation in both native245

(light) and heavy PNP.246

4.2. TPS predictions247

Our simulations of the designed heavy F159Y PNP mutant showed that the248

dynamics of the His257-O5′–O4′ compression that had been altered by the iso-249

topic substitution in the heavy PNP was restored (Table 4). Both light and heavy250

F159Y PNPs achieve full O5′–O4′ compression comparable to that of native light251

PNP (compare to Table 1). However, in the light F159Y there is a mistiming as252

the O5′–O4′ compression is not coordinated with TS barrier crossing, but instead253

happens well before TS formation.254

In Figure 5 we show contour maps of the O5′–O4′ distance as a function of the255

progression of a reaction coordinate defined as the difference of the bond breaking256

10

Figure 4: Catalytic site of the F159Y PNP mutant, including residues Asn243, His257, and thePhe159 contributed from the neighboring monomer.

O5′–O4′ time (fs) separatingminimum distance (Å) minimum distance from TS

F159Y L mutant 2.56 ± 0.10 −40 to −15 fsF159Y H mutant 2.54 ± 0.06 −16 to −4 fs

Table 4: Minimal values of the O5′–O4′ distance averaged over all trajectories and range of timeseparation from minimum to TS crossing

C1′–N9 minus the bond forming C1′–OP distances. These contour maps repre-257

sent histograms of these distances from all slices of the reactive trajectories we258

generated. The plots identify the most probable paths of reaction in the plane259

of the O5′–O4′ compression distance vs the bond breaking minus bond forming260

distances.261

For native PNP the O5′–O4′ region has high density at 3 Å for the reac-262

tant state, and it is compressed as reactive trajectories approach the TS, where263

it reaches a minimum of 2.56 Å (Table 1 and panel A of Figure 5). On the other264

hand, in heavy PNP the O5′–O4′ distance has high density at 2.5 Å for reactants265

and increases as the reaction progresses, reaching a value of 2.94 Å at the TS266

(panel B of Figure 5).267

For the light F159Y PNP, the O5′–O4′ distance has high density at 3.3–3.6 Å268

for reactants and is slightly compressed as reactive trajectories approach the TS269

(panel C of Figure 5). Heavy F159Y reactive trajectories follow similar paths as270

in the native enzyme, with the O5′–O4′ reactant distance having a high density at271

11

Figure 5: Projections of histogrammed densities of the structures along all reaction trajectories onthe plane of the O5′–O4′ oxygen distance vs. bond breaking (BB)–bond-forming (BF) distance,for (A) native light PNP, (B) native heavy PNP, (C) light F159Y PNP, and (D) heavy F159Y PNP.

12

kcat (s−1) KM(µM) kcat/KM (M−1 s−1) kchem (s−1) on-enzyme KIE

WTL 8.7 ± 0.2 34.1 ± 2.1 2.5 × 105 ± 0.2 263 ± 9 1.31 ± 0.06WTH 7.8 ± 0.3 39.9 ± 4.3 2.0 × 105 ± 0.2 200 ± 6MutL 8.5 ± 0.3 56.4 ± 5.3 1.5 × 105 ± 0.2 8.3 ± 0.4 0.75 ± 0.04MutH 8.3 ± 0.4 54.2 ± 5.7 1.5 × 105 ± 0.2 11.1 ± 0.2

Table 5: Enzyme kinetic parameters of light and heavy PNPs.

3.25 Å and reaching a minimum of 2.60 Å at the TS (panel D of Figure 5).272

The difference in the dynamical behavior of the His257-linked compression273

between heavy and light F159Y PNP is related to the probability of TS formation274

and partially explains the improved barrier crossing rate (discussed in the experi-275

mental subsection below) for heavy F159Y compared to the light F159Y.276

Another important residue whose distances we monitored is Asn243, which277

hydrogen-bonds with the guanine leaving group. We examined the differences278

in interactions between Asn243 and the purine leaving group for light and heavy279

F159Y PNPs. In the heavy F159Y this distance for the TS was 2.82 Å, more280

favorable than in light F159Y PNP where it was 3.8 Å placing Asn243 far away281

from the guanosine leaving group at the TS. Since Asn243 is important for stabi-282

lizing the leaving group, this difference between light and heavy F159Y possibly283

contributes as well to the inverse heavy-atom isotope effect that we describe next.284

4.3. Effects of F159Y Mutation on Kinetics.285

Experimental analysis of the heavy and light F159Y PNPs by our collaborators286

[38] is in agreement with the TPS simulations. The enzymatic kinetic parameters287

for the light, heavy and mutant enzymes are given in Table 5. The F159Y muta-288

tion in PNP did not alter the steady-state kcat values. However, pre-steady state289

measurements comparing native and F159Y PNPs indicated a decrease in the rate290

of the chemical step by a factor of 32 in F159Y PNP.291

The heavy enzyme isotope effect klightchem / kheavy

chem for native PNP was 1.31, while292

for the two F159Y enzymes it was 0.75, i.e. an inverse isotope effect.293

4.4. Summary294

In heavy enzyme the increase in mass alters the dynamical search for the TS,295

decreasing the probability of barrier crossing, leading to a normal kinetic isotope296

effect (i.e. > 1). Using insights from atomistic details of trajectories harvested by297

TPS simulations, we designed a simply modified PNP, where a F159Y mutation298

13

was expected to increase the probability of TS formation. The mutation restored299

important femtosecond motions and exhibited faster chemistry in the catalytic step300

for the heavy mutant PNP compared to the light mutant.301

5. PNP design III: Designed heavy enzyme faster than the native [20]302

Motivated by our previous successful attempt, where mutating Phe159 to Tyr303

(F159Y) created an enzyme where the fast dynamics of the heavy enzyme was304

more likely to find the transition state than in its natural isotopic form, and since305

there were strong indications of the catalytic role of Asn243 (which had been306

also confirmed experimentally [41] since the mutation Asn243Ala decreases the307

catalytic efficiency by 3 orders of magnitude) we computationally labeled all As-308

paragines in the heavy enzyme.309

PNP has eleven Asn residues, ten located distant from the catalytic site and310

only Asn243 is in the active site in direct contact with the leaving group. Asn243311

stabilizes the N7-protonated purine ring, thereby activating the leaving group. We312

created two enzymes in silico: a heavy-Asn243 light PNP (AsnH–PNPL) and a313

light-Asn243 heavy PNP (AsnL–PNPH).314

The kinetic parameters, as measured by our collaborators [20], for the light,315

heavy and mutant enzymes are shown in Table 6. Steady-state kinetics is reflected316

on kcat and pre-steady-state kinetics on kchem. When only Asn were labeled, ex-317

periments found faster chemistry (an inverse isotope effect), indicating that a PNP318

fully labeled except at the Asparagines would show even slower catalytic site319

chemistry than the fully labeled heavy PNP.320

kcat (s−1) KM(µM) kcat/KM (M−1 s−1) kchem (s−1) on-enzyme KIE

Native PNP 7.2 ± 0.3 38.9 ± 4.4 1.9 × 105 ± 0.2 191 ± 8AsnH–PNPL 6.8 ± 0.2 43.4 ± 3.5 1.6 × 105 ± 0.1 246 ± 9 0.79 ± 0.04AsnL–PNPH 7.2 ± 0.3 39.0 ± 4.4 1.8 × 105 ± 0.1 270 ± 11 0.71 ± 0.04

Table 6: Enzyme kinetic parameters of light and isotopically labeled PNPs.

Unexpectedly, the enzyme AsnL–PNPH that has heavy amino acids through-321

out except for the light Asp, has faster chemistry at the catalytic site This rare322

case of catalytic site activation demonstrates that the masses of both primary and323

secondary sphere amino acids affect the catalytic site contacts. than the native324

enzyme. This rare case of catalytic site activation demonstrates that the masses of325

14

both primary and secondary sphere aminoacids affect the catalytic site contacts.326

The computational analysis in the next subsection reveals the atomistic details of327

the fast dynamic mechanism for the unusual inverse heavy enzyme isotope effects328

in the AsnH–PNPL and AsnL–PNPH enzymes.329

5.1. Computational Analysis330

We employed transition path sampling to generate and analyze reactive tra-331

jectories and the transition state ensemble. We analyzed all the important dis-332

tances between the substrate and the reaction coordinate residues. We performed333

constrained molecular dynamics calculations at a ps scale for each of the three334

enzymes (native PNP, AsnH–PNPL and AsnL–PNPH) to monitor how active site335

interactions lead to transition state formation.336

Starting from the structure in the reactive trajectory that is 10 fs before the337

TS, we performed a constrained propagation of the system for 5 ps: we restrained338

motions of the substrate with protonated N7-guanosine, and HPO2−4 groups by339

applying a restraining harmonic force, while the rest of the protein could move340

freely. During this constrained propagation we measured the distances between341

important reaction coordinate residues and the substrate, and tabulated the range342

of the variation of these distances. We were especially interested in the interaction343

of Asn243 with the leaving group.344

The carbonyl oxygen OD1 of the Asn243 sidechain stabilizes protonation of345

N7, and the nitrogen amide (ND2) forms a hydrogen bond to the O6 carbonyl oxy-346

gen of guanine. As shown in Figure 6, the distance OD1–N7 periodically reaches347

a minimum of ≤ 2.50 Å in native PNP. It is not improved in AsnH–PNPL (2.53 Å),348

but is improved by 0.13 Å in AsnL–PNPH (Table 7). However, the ND2—O6 in-349

teraction improves significantly in both heavy Asn enzymes, by 0.36 Å in AsnH–350

PNPL and by 0.31 Å in AsnL–PNPH (Table 7). Also, optimal interactions between351

ND2–O6 of Asn243 ( ≤ 2.5 Å) to occur more frequently in both mutated en-352

zymes, which indicates that this mass-altered promoting vibration is a link to the353

increased rate of chemistry in AH–PNPL and AL–PNPH.354

15

0 1000 2000 3000 4000 5000time (fs)

2

2.5

3

3.5

4

dist

ance

(Å

)

OD1-N7ND2-O6Native PNP

1 excursion to 2.5 Å

A

0 1000 2000 3000 4000 5000time (fs)

2

3

4

5

6

7

dist

ance

(Å

)

OD1-N7ND2-O6Heavy ASN, light PNP

7 excursions to 2.5 Å

B

0 1000 2000 3000 4000 5000time (fs)

2

2.5

3

3.5

4

4.5

5

dist

ance

(Å

)

OD1-N7ND2-O6Light Asn, heavy PNP

10 excursions to 2.5 Å

C

Figure 6: Asn243 interactions to guanine N7 and O6 of the transition state ensemble: (A) NativePNP, (B) AsnH–PNPL; (C) AsnL–PNPH. Interactions that form activating hydrogen bonds of≤ 2.5 Å occur more frequently in the heavy enzymes.

16

OD1–N7/Asn243 ND2–O6/Asn243

Native PNP 2.50 – 3.01 2.72 – 3.55AsnH–PNPL 2.53 – 4.31 2.36 – 6.05AsnL–PNPH 2.37 – 4.44 2.41 – 4.45

Table 7: Ranges (in Å) of interaction distances between reactant atoms of the substrate and atomsof residue Asn243 (averages of 10 simulations of 5 ps).

Glu201 forms hydrogen bonds with the guanine leaving group and shows355

slight improvement in its contact minima (0.14 and 0.03 Å) in the Asn constructs356

(Table 8). Of the four phosphate interactions (Tyr88, Ser220, Ser33 and His86),357

only Ser220 shows improvement in both heavy PNPs, but this is a weak interac-358

tion with minima at 3.37 and 3.51 Å (Table 9).359

OD1–O5/His257 OE2–N2/Glu201 OH–O3′/Tyr88

Native PNP 2.45 – 3.02 2.52 – 3.69 2.48 – 3.22AsnH–PNPL 2.44 – 4.89 2.38 – 3.74 2.58 – 5.27AsnL–PNPH 2.48 – 4.44 2.49 – 3.73 2.38 – 3.87

Table 8: Ranges (in Å) of distances between reactant substrate atoms and atoms of residues in-volved in forming the transition state of PNP.

OG–O2′ Ser220 N–O1 Ser33 NE2–O2 His86

Native PNP 4.03 – 4.66 2.72 – 3.58 4.61 – 5.75AsnH–PNPL 3.37 – 4.98 3.02 – 5.20 3.81 – 5.61AsnL–PNPH 2.51 – 4.86 2.66 – 4.01 2.89 – 4.90

Table 9: Ranges (in Å) of distances for enzyme to reactant atoms involved in the transition stateof PNP.

5.2. Summary360

In fully or partially His-labeled heavy PNPs, it has been shown that increased361

mass leads to an increase of the barrier to TS formation, resulting in a decrease362

of the rate of the chemical step, However, we showed that when PNP is labeled363

with heavy Asparagines, an inverse isotope effect is found, indicating an increase364

17

of the barrier crossing probability in AsnH–PNPL. Transition path sampling cal-365

culations support this finding by demonstrating altered femtosecond catalytic site366

motions with improved Asn243 interactions to the purine leaving group. The re-367

sults with partially labeled PNPs provide additional support for the role of fast368

protein dynamics: they create the correct geometry for forming the electrostatic369

environment for transition state formation.370

6. Concluding Remarks371

We showed that atomistic detail information obtained by combined transi-372

tion path sampling simulations and experimental work on Born-Oppenheimer en-373

zymes, can pinpoint residues that are good candidates for mutations. A sequence374

of three investigations on using information for protein motions in PNP that are375

coupled to the TS barrier crossing led to the design of an enzyme whose chemical376

step rate is faster than the native PNP.377

Acknowledgements378

We gratefully acknowledge our experimental collaborator Vern Schramm for379

illuminating experiments and discussions on all aspects of rate promoting motions380

and enzymatic catalysis. All computer simulations were performed at the Univer-381

sity of Arizona High Performance Computing Center, on a SGI Altix ICE 8400382

supercomputer and a Lenovo NeXtScale nx360 M5 supercomputer. This research383

was supported through the NIH program project grant GM068036.384

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