the involvement of 
 protein motions in the chemical step of enzyme 
 reactions that involve hydrogen ( h , h , or h ) tunnelling remains one of the most discussed 
 topics in modern enzymology . early computational evidence suggested 
 that dynamic effects may not be required to account for enzymatic 
 catalysis and that the participation of protein motions in the chemical 
 step can be satisfactorily described as equilibrium fluctuations . nevertheless , theoretical frameworks that involve 
 protein  promoting vibrations  or  promoting 
 motions  on femtosecond to millisecond time scales , which are 
 proposed to reduce the height and/or width of the potential energy 
 barrier and thereby enhance enzymatic catalysis , have been invoked 
 to interpret experimental data . protein motions occur over a hierarchy of time scales and ranges , from femtosecond local bond vibrations to millisecond large scale 
 domain motions . it has been suggested that motions on one time scale 
 may facilitate motions on another . a number of 
 theoretical analyses based on atomistic simulations have suggested 
 that protein motions may not significantly contribute to reducing 
 the free energy barrier of enzyme catalyzed reactions , and several experimental studies have shown that models which require 
 a contribution from protein motions for catalysis do not seem fully 
 compatible with the available data . a combination of experimental results , qm / mm simulations , and theoretical 
 analyses has however recently revealed that the dynamics of the protein 
 environment do have a small but measurable effect on the chemical 
 reaction . dihydrofolate reductase 
 ( dhfr ) has often been used in studies of 
 the relationship between protein motions and catalysis . it catalyzes the nadph - dependent reduction of 7,8-dihydrofolate 
 ( h2f ) to 5,6,7,8-tetrahydrofolate ( h4f ) by hydride 
 transfer from c4 of nadph and protonation of n5 of h2f 
 ( figure 1 ) . the catalytic cycle of dhfr from e. coli ( ecdhfr ) has been thoroughly characterized ; the physical steps of substrate binding and product release involve 
 large scale millisecond time scale conformational motions of the m20 
 loop ( residues 924 ) , which forms part of the active site . the closed conformation , found in the holo - enzyme and the michaelis 
 complex , is stabilized by hydrogen bonding 
 from the m20 loop to the neighboring fg loop ( residues 116132 ) . following hydride transfer , the m20 loop adopts the occluded conformation , 
 which is stabilized by hydrogen bonds from the m20 loop to the neighboring 
 gh loop ( residues 142149 ) . this prevents the nicotinamide 
 ring of the cofactor nadp(h ) from entering the active site ( figure 1 ) . a recent 
 report of a  dynamic knockout  of ecdhfr 
 has reignited controversy over the role of protein motions in hydrogen 
 transfer reactions . ecdhfr - n23pp / s148a 
 is unable to adopt the occluded conformation due to the absence of 
 the crucial hydrogen bonds between the m20 and gh loops , and 
 millisecond to microsecond time scale motions observed in the m20 
 loop of wild type ecdhfr are lost in the variant . this  dynamic knockout  displayed reduced 
 hydride transfer rate constants , and it was proposed that the protein 
 motions lost in ecdhfr - n23pp / s148a are involved in promoting hydride 
 transfer in wild type ecdhfr . however , 
 theoretical studies based on the empirical valence bond approach suggested 
 that the reduction in the hydride transfer rate constant in ecdhfr - n23pp / s148a 
 was due to effects on the electrostatic preorganization and consequently 
 the reorganization free energy within the active site . measurement of the kinetic isotope effects of 
 the ecdhfr - n23pp / s148a catalyzed hydride transfer reaction provided 
 further evidence that the loss of protein motions may not be the cause 
 of the impaired catalysis . a number of 
 other studies have also suggested that protein motions do not promote 
 the chemical step in wild type ecdhfr catalysis , but the issue continues to generate debate in the literature . ( a ) conversion 
 of dihydrofolate to tetrahydrofolate through transfer 
 of the pro - r hydride of nadph and a solvent proton . catalytically 
 important loops ( m20 , fg , and gh ) , substrate ( h2f ) , and cofactor ( nadph ) are labeled . the m20 loop is highlighted 
 in red in the closed conformation and in blue in the occluded conformation . oppenheimer approximation 
 assumes that , while isotopic 
 substitutions do not affect the electronic potential energy surface , 
 mass - dependent differences result in changes in atomic motions from 
 femtosecond bond vibrations to millisecond time scale conformational 
 changes . hence , enzymatic isotopic substitution 
 to form  born  oppenheimer enzymes  has been postulated to affect catalysis by changing protein motions 
 that couple to the reaction coordinate . accordingly , we have recently 
 shown by a combination of experimental and computational studies of 
 light ( natural isotopic abundance ) and heavy ( n , c , h isotopically substituted ) ecdhfr that mass - dependent 
 protein motions in ecdhfr affect the dynamic recrossing of hydride 
 transfer but they do not promote tunnelling , and that the increased 
 number of recrossing trajectories has a slight effect on the effective 
 barrier of the chemical step . the 
 present investigation analyzes the dynamic contributions to 
 enzyme catalysis by comparing heavy ecdhfr - n23pp / s148a with its light 
 counterpart . in particular , we report experimental and computational 
 results that allow characterization of the dynamics of the coordinates 
 associated with the hydride transfer from nadph to h2f . 
 we provide strong evidence that the loss of protein motions observed 
 previously by nmr does not directly impact 
 catalysis of the hydride transfer step ; in fact , the chemical step 
 is subject to greater dynamic contributions in the 
  dynamic knockout  than in the wild type enzyme . together 
 with the increased reaction barrier , the increased dynamic coupling 
 to the chemical coordinate is the cause of the reduction of the hydride 
 transfer rate observed in ecdhfr - n23pp / s148a . ecdhfr - n23pp / s148a was produced in m9 medium 
 containing exclusively nh4cl , u after purification in buffers made of h2o , 
 heavy ecdhfr - n23pp / s148a showed a 10.02% increase in molecular mass 
 ( figures s1 and s2 , supporting information ) , indicating that 91.2% of the n , c , and 
 non - exchangeable h atoms had been replaced by their heavier 
 isotopes . the secondary structures of light and heavy ecdhfr - n23pp / s148a 
 were indistinguishable as measured by circular dichroism spectroscopy 
 ( figure s3 , supporting information ) . the nature of the rate limiting 
 step in dhfr catalysis is dependent on ph . at ph 7 , the release of nadp from the binary ecdhfr - n23pp / s148anadp complex is most likely rate limiting , whereas the release of h4f from the enadphh4f mixed ternary complex is rate limiting in wild type ecdhfr . neither the michaelis constants km nor the turnover numbers kcat were sensitive to isotopic substitution of ecdhfr - n23pp / s148a ( tables 
 s2 and s3 , supporting information ) . in 
 the ecdhfrnadp complex as well as in the apoenzyme , 
 the loop regions are largely disordered and hence nadp release is unlikely to involve a significant 
 conformational change in either the wild type or variant enzyme . in 
 contrast , a significant enzyme kiecat ( kcat / kcat , where le and he indicate light and heavy enzyme , respectively ) 
 on the steady - state rate constants for wild type ecdhfr of 1.16  
 0.01 at 35 c was observed , consistent 
 with the large conformational change observed on h4f release . for ph values above 9 , the steady - state rate constants 
 measured at ph 9.5 for light and heavy ecdhfr - n23pp / s148a showed a 
 temperature dependent enzyme kiecat , such that kcat is 14% larger than kcat at 10 c and 34% larger 
 at 40 c ( figure 2 , tables s1 and s2 , supporting information ) . the enzyme kie was higher 
 in ecdhfr - n23pp / s148a than in wild type ecdhfr at all temperatures . in contrast , the michaelis constants for nadph and for h2f are unaffected by isotopic substitution at both 20 and 35 c 
 ( table s3 , supporting information ) , indicating 
 that binding interactions are unchanged in the heavy enzyme and therefore 
 that , at ph 9.5 , the enzyme kie reflects a difference in reactivity 
 between the light and heavy enzymes after the formation of the respective 
 michaelis complexes . temperature dependence of the experimental ecdhfr - n23pp / s148a 
 hydride 
 transfer rate constants . ( a ) ph 9.5 steady state kinetic data ; ( b ) 
 ph 7.0 pre - steady - state kinetic data . data and arrhenius fits are 
 shown in red for the light enzyme and in blue for the heavy enzyme . ( c and d ) the enzyme kie ( ratio of light to heavy enzyme rate constants , k / k ) at ph 9.5 
 and ph 7.0 , respectively . data for light and heavy wild 
 type ecdhfr are from ref ( 28 ) . hydride transfer 
 at ph 9.5 is not physiologically significant , so the rate constants of the fast hydride transfer 
 from reduced nadph to mostly protonated h2f were determined 
 at ph 7.0 in pre - steady - state stopped - flow experiments , in which the 
 fluorescence resonance energy transfer from the protein to reduced 
 nadph was measured . the ph dependence of the pre - steady - state hydride 
 transfer rate constants indicated that the apparent pka of the ecdhfr - n23pp / s148a catalyzed reaction was not 
 affected by isotopic substitution ( figure s4 and table s4 , supporting information ) . the apparent pka values for the reactions catalyzed by light 
 and heavy ecdhfr - n23pp / s148a were 6.29  0.10 and 6.23  
 0.09 at 20 c and 6.35  0.16 and 6.15  0.05 at 35 
 c . the hydride transfer rate constants for light and heavy ecdhfr - n23pp / s148a 
 ( kh and kh ) at ph 7.0 show a similar dependence on 
 temperature to that observed in the steady state measurements at elevated 
 ph ( table s1 , supporting information ; figure 2 ) . the enzyme kieh ( kh / kh ) increased from 1.31  0.03 at 10 c to 1.43  0.04 
 at 40 c ( figure 2 ) . these are significantly 
 higher than the corresponding values of 0.93  0.02 at 10 c 
 to 1.18  0.09 at 40 c reported previously for the reaction 
 catalyzed by wild type ecdhfr . activation 
 energies were slightly higher in light ecdhfr - n23pp / s148a than in 
 the heavy counterpart , with the reduction in free energy for the reaction 
 resulting from lower arrhenius prefactors and hence a less favorable 
 activation entropy ( table 1 ) . the same situation 
 had also been observed in the reaction catalyzed by wild type ecdhfr . the reduced rate constants for hydride transfer 
 in ecdhfr - n23pp / s148a relative to ecdhfr have also been shown to be 
 the result of less favorable activation entropy in the variant , rather 
 than increased activation enthalpies . our analysis of the rate constant of the chemical step is based 
 on transition state theory ( tst ) , modified to account for tunnelling 
 contributions and other dynamic effects:1where r is the ideal gas 
 constant , t is the temperature , kb is the boltzmann constant , h is planck s 
 constant , gactqc(t , z ) is 
 the quasi - classical activation free energy ( for details , see the supporting information ) obtained as a function of a reaction coordinate z that corresponds to the transfer of the hydride from the donor atom 
 of the cofactor to the substrate s acceptor atom ( z = d(c4nadph  ht ) ht ) ) , and (t , z ) is the temperature - dependent transmission 
 coefficient , which contains the dynamic corrections to the classical 
 rate constant and is therefore equal to unity in the limit of classical 
 tst . although different contributions are in principle coupled , (t , z ) can be expressed as2where (t , z ) is the recrossing transmission coefficient 
 that 
 corrects the rate constant for trajectories that recross the dividing 
 surface back to the reactant valley and (t ) is the tunnelling coefficient that accounts for reactive trajectories 
 that do not reach the classical threshold energy . because the definition 
 of the selected reaction coordinate ( z ) involves 
 only coordinates of atoms from the reacting subsystem ( substrate and 
 cofactor ) , the dynamic impact of protein motions in the chemical step the two terms of eq 2 can be obtained from qm / mm 
 simulations ( for details , see the supporting information ) . the same approach has previously been used to analyze the reactivity 
 of wild type ecdhfr . the calculated 
 rate constants for wild type ecdhfr ( table 2 ) are in excellent agreement with the experimental data , while the values calculated for ecdhfr - n23pp / s148a 
 are somewhat smaller than those measured by experiment . this is most 
 probably due to a small systematic error in the energy function that 
 leads to an overestimation of the free energy barrier . however , the 
 difference is below 1 kcalmol and of the 
 same order of magnitude as the statistical uncertainty associated 
 with the free energies ( table 2 ) . the calculations 
 show clearly that the reduction in the rate constant in ecdhfr - n23pp / s148a 
 relative to the wild type enzyme is essentially due to the increase 
 in the quasi - classical activation free energy ( table 2 ) , while the recrossing transmission coefficients are similar 
 but distinct and tunnelling contributions are also very close in both 
 wild type and variant enzyme ( table 2 ) . these 
 results support the previous conclusions that the reduction in the 
 rate constant in ecdhfr - n23pp / s148a is not due to the impact of a 
  dynamic knockout  on the chemical step but to a change 
 in the properties of the equilibrium in the reactant state ( rs ) and 
 transition state ( ts ) ensembles . protein 
 and protein  substrate / cofactor interactions that affect the 
 free energy barrier . comparison of heavy and light ecdhfr and 
 ecdhfr - n23pp / s148a shows 
 that the difference in phenomenological rate constants between isotopomers 
 arises from differences in the recrossing coefficients (  ) . 
 tunnelling contributions (  ) are not affected by the change 
 in mass between the light and heavy enzymes , which is not in agreement 
 with proposals of tunnelling enhancement by dynamic coupling . according to our simulations , such compressive  promoting motions need not be invoked to explain the observed changes in reactivity ; 
 this finding is in agreement with recent work that revealed that  promoting 
 vibrations  do not drive hydride transfer in the active site 
 of ecdhfr . however , the value of the 
 recrossing transmission coefficient (  ) reflects the subtle 
 coupling of protein environmental motions to the reaction coordinate 
 in a way that is only apparent via a global description of all atomic 
 positions . when the mass of the enzyme is increased , these motions 
 are slower and the chemical system is not so efficient in relaxing 
 to the reactant or product valleys after crossing the ts . this leads 
 to an increase in the number of recrossings and therefore a reduction 
 of the value of  in the heavy enzyme relative to its light 
 counterpart . simulations successfully reproduce the larger enzyme 
 isotope effects 
 obtained experimentally for the variant ( table 2 ) . the computed k / k values for the variant and wild type enzymes are 1.26 
 and 1.16 , while the experimental values are 1.37 and 1.10 . the increased 
 enzyme kie for ecdhfr - n23pp / s148a relative to the wild type provides 
 strong support for enhanced coupling of protein environmental motions 
 to the reaction coordinate in the variant so that the chemical step 
 becomes more sensitive to global protein motions in the modified enzyme . our results show that the dynamic impact of protein motions on the 
 chemical step is in fact larger in ecdhfr - n23pp / s148a than in the 
 wild type enzyme , as reflected by the larger deviation from unity 
 observed in the recrossing transmission coefficients of 0.53 and 0.42 
 for light and heavy ecdhfr - n23pp / s148a versus 0.57 and 0.49 for light 
 and heavy ecdhfr . further simulations were conducted to rationalize 
 this unexpected behavior of the  dynamic knockout  variant . to 
 gain insight into the role of protein motions in ecdhfr and ecdhfr - n23pp / s148a , 
 simulations of the free energy landscape of the enzymes were performed . free energy surfaces ( fess ) for hydride transfer in wild type ecdhfr 
 and ecdhfr - n23pp / s148a and in the absence of an enzyme in aqueous 
 solution were traced as a function of two coordinates ( figure 3 ; see the supporting information for details ) , namely , the solute ( or chemical ) coordinate ( z ) that corresponds to the transfer of the hydride and a 
 solvent ( or environmental ) coordinate ( s ) that captures 
 those environmental motions relevant for the chemical process . this coordinate is obtained as the antisymmetric 
 combination of the electrostatic potential created by the protein 
 and aqueous environment on the donor and acceptor carbon atoms ( s = v(c4nadph ) v(c6h2f ) ) and is analogous to the solvent polarization 
 in marcus theory of electron transfer reactions . transmission 
 coefficient components 
 due to recrossing (  ) and tunnelling (  ) , quasi - classical 
 ( qc ) free energy of activation ( gactqc ) ( eq 1 ) , effective phenomenological free energies of activation 
 ( geff ) , and predicted ( ktheor , at 300 k ) and experimental ( kh , at 303 k ) hydride transfer rate constants are included . components of the 
 quasi - classical activation free energy , the potential of mean force 
 ( pmf ) difference between the ts and the reactants , and the classical 
 and quantized vibration corrections are reported in the supporting information . data for light and heavy 
 wild type ecdhfr are from ref ( 28 ) . a more complete 
 description of the chemical process can be obtained 
 by following the minimum free energy paths traced on the fess ( figure 3 ) . in all cases , the reaction starts with a change 
 in the solvent coordinate , then essentially moves along the chemical 
 coordinate to pass through the ts , and finishes with a new change 
 in the solvent coordinate , leading to the relaxed products . thus , 
 the reaction proceeds with participation of the solvent coordinate , 
 mostly before and after crossing the ts region . this explains the 
 small deviation from unity observed in all the recrossing transmission 
 coefficients reported in the previous section . environmental 
 motions involved in the evolution from the michaelis 
 complex to the ts can be characterized by means of the frequency associated 
 with the solvent coordinate . to this end , the force constants were 
 evaluated from a parabolic fit of the free energy landscape along 
 the solvent coordinate and the associated effective masses were derived 
 from the equipartition theorem . from these data , the resulting frequencies 
 for the three environments can be calculated . the values of the force 
 constants found for the enzymes ( 2.4  10 and 2.3 
  10 kcalmole for ecdhfr and ecdhfr - n23pp / s148a , respectively ) are significantly 
 larger than those for aqueous solution ( 2.6  10 kcalmole ) . this is to be expected , 
 as deforming the environment is energetically more demanding in enzymes 
 than in solution due to the existence of a covalent structure in the 
 proteins that does not exist in solution . as observed , the mass associated 
 with the solvent coordinate is also significantly larger in the case 
 of the two enzymes ( 1.2  10 and 1.3  10 kcalmoles for ecdhfr and ecdhfr - n23pp / s148a , respectively ) than in 
 solution ( 2.6  10 kcalmoles ) . the combined effect of the larger force 
 constants and the larger associated mass for the enzymes means that 
 the frequencies associated with the environmental motions are similar 
 in all scenarios , and practically identical in ecdhfr and ecdhfr - n23pp / s148a 
 ( 240 cm in ecdhfr , 230 cm in 
 ecdhfr - n23pp / s148a , and 170 cm in solution ) . thus , 
 environmental motions relevant for the hydride transfer have similar 
 time scales in the three cases ( of the order of picoseconds or faster ) . 
 analysis of these frequency modes reveals them to be associated with 
 hydrogen bond pattern rearrangement around the chemical system ( substrate 
 and cofactor ) . the characteristic frequencies obtained for the solvent 
 coordinate in the variant dhfr are not consistent with a mutation - induced 
 change of the protein dynamics that could have noticeable consequences 
 for the rate of hydride transfer . picosecond time 
 scale motions are the motions that can couple to the chemical step . this finding does however not exclude an effect from the mutations 
 on the millisecond protein dynamics , but 
 such changes of the dynamics do not affect crossing of the barrier 
 to hydrogen transfer . the decrease in the rate constant observed 
 in ecdhfr - n23pp / s148a 
 relative to the wild type enzyme can be attributed almost exclusively 
 to an increase in the quasi - classical activation free energy of the 
 chemical step ( table 2 ) . introducing mutations 
 into the enzyme can provoke changes in the rs and/or ts ensembles 
 and thus in the free energy differences between them . an analysis 
 of averaged geometries has been carried out from 2 ns qm / mm md simulations 
 at the ts and rs of ecdhfr and ecdhfr - n23pp / s148a . in the case of 
 ecdhfr - n23pp / s148a , the mutations alter some protein  protein 
 and protein  cofactor interactions established by residues belonging 
 to the m20 loop at the reaction ts ( table s5 , supporting information ) . in particular , the averaged glu17nhoasp122 
 distance at the ts of ecdhfr - n23pp / s148a is 2.4  0.6  , 
 while this hydrogen bond interaction between the m20 and fg loops 
 is significantly weaker in the ts of wild type ecdhfr ( the averaged 
 distance is 4.0  0.7  ) . the fact that this hydrogen bond 
 is strongly formed only in the ts of ecdhfr - n23pp / s148a could contribute 
 to the smaller enthalpic and larger entropic barrier found experimentally 
 for the variant . free energy surfaces 
 corresponding to the hydride transfer from 
 nadph to protonated h2f in aqueous solution ( left ) , wild 
 type ecdhfr ( middle ) , and ecdhfr - n23pp / s148a ( right ) . the dotted lines represent the minimum free energy paths on 
 the free energy surfaces obtained from the gradient of the surface . other changes in the interactions 
 established by the m20 loop with 
 the cofactor or the substrate are observed upon mutation . met20 has 
 a reduced capability to form a shn hydrogen bond 
 with the amide group of the cofactor at the ts in the variant . the 
 averaged distances are 2.6  0.3 and 3.0  0.4  in 
 the tss of ecdhfr and ecdhfr - n23pp / s148a , respectively ( table s5 , supporting information ) . from an electronic point 
 of view , the formation of this hydrogen bond favors hydride transfer 
 from the cofactor to the substrate . met20 
 has also been proposed to play an important role at the cofactor / substrate 
 interface . dihedral angles of the met20 
 side chain ( figure s7 and table s5 , supporting 
 information ) show the preference for different conformations 
 of these residues in the wild type and variant enzymes . in support 
 of these findings , differences in the positioning of the sulfur atom 
 of met20 and in the preferred conformation of its side chain between 
 wild type ecdhfr and ecdhfr - n23pp / s148a finally , other residues of the m20 loop such 
 as asn18 and ala19 are farther from the cofactor at the ts of the 
 variant than in wild type ecdhfr ( table s5 , supporting 
 information ) , confirming the disruption of stabilizing interactions 
 established by this loop in the ts by mutating the enzyme . differences 
 in the equilibrium fluctuations of the protein residues 
 between wild type and variant were analyzed from the 2 ns qm / mm md 
 simulations of the ts by means of the root - mean - squared fluctuation 
 ( rmsf ) of all residues of the proteins . the differences observed between 
 the rmsf of residues in ecdhfr and ecdhfr - n23pp / s148a ( figure 4 ) are never larger than 0.5  in absolute value . thus , both proteins show similar flexibility on the time scale relevant 
 to catalysis ( vide supra ) including in the flexible 
 fg , gh , and m20 loops ( figure 4a ) . this result is in agreement with a recent evolutionary study 
 of dhfrs from different species , which showed that mutations do not 
 cause large changes to the equilibrium fluctuations but that subtle 
 changes to the equilibrium conformational sampling alter the free 
 energy barrier of the enzymatic reaction , as reflected also in our results ( table 2 and table s5 , supporting information ) . our simulations demonstrate that residues in the active site are slightly 
 more mobile for ecdhfr - n23pp / s148a than for the wild type enzyme in 
 the ts ( figure 4b ) , reflecting the fact that 
 protein  substrate interactions established in the active site 
 at the ts are not as well optimized in the variant . this is consistent 
 with a recent computational analysis of x - ray crystallographic results , 
 which shows increased conformational heterogeneity in the active site 
 of ecdhfr - n23pp / s148a compared to the wild type enzyme . while differences between the rate constants 
 of ecdhfr and ecdhfr - n23pp / s148a 
 are mostly due to changes in the equilibrium properties of the enzymes , 
 the fact that the active site of the variant is less well set up for 
 catalysis than the active site of the wild type also has an impact 
 on protein motions coupled to the reaction , as previously deduced 
 from the comparison of the recrossing transmission coefficients ( table 2 ) . the connection between mutations and dynamics 
 can be rationalized observing the behavior of the environmental coordinate 
 in the fess ( figure 3 ) . the ordering of the 
 barriers without vibrational corrections is 14.6 , 17.5 , and 23 kcalmol for ecdhfr , ecdhfr - n23pp / s148a , and the reaction 
 in aqueous solution , respectively . these values can be correlated 
 with the displacement along the solvent coordinate s needed to reach the ts from the rs ( s = s(ts ) the s values obtained 
 from the fess for the reaction in ecdhfr , ecdhfr - n23pp / s148a , and 
 in solution are 5 , 7 , and 27 kcalmole , respectively . while the two enzymes stabilize the 
 rs at a solvent coordinate closer to the value needed to reach the 
 ts , in aqueous solution the reactants are found at a much larger value 
 of s ( 40 kcalmole ) . that is , at the rs , both enzymes already 
 provide an environment much more conducive to hydride transfer than 
 in aqueous solution . in other words , interestingly , the reorganization 
 needed to reach the ts is larger for the variant than the wild type , 
 as reflected in the larger value of s . hence , the participation of protein motions in the 
 reaction coordinate in ecdhfr - n23pp / s148a is larger than that in wild 
 type ecdhfr . this observation agrees with the relative values of the 
 recrossing transmission coefficients ( table 2 ) for the variant and the wild type that reflect a larger impact 
 of protein motions in the former . thus , mutations that reduce the 
 catalytic properties of the enzymatic active site increase the participation 
 of protein motions in the chemical step because the new active site 
 requires a larger rearrangement to reach the ts . differences of the femtosecond  picosecond 
 root - mean - square 
 fluctuations ( rmsfs ) between ecdhfr - n23pp / s148a and ecdhfr calculated 
 for the backbone ca atoms in the tss . ( b ) projection on the protein backbone using a color scale : 
 red represents regions of the protein that are more mobile in the 
 ecdhfr than in ecdhfr - n23pp / s148a , while blue represents the opposite 
 behavior . the 
 present investigation has used a combination of experimental 
 and computational techniques to analyze the dynamic contributions 
 to catalysis in ecdhfr - n23pp / s148a by comparing the heavy ( n , c , h isotopically substituted ) enzyme 
 with its light ( natural isotopic abundance ) counterpart . the good 
 agreement between the experimental and computationally derived results interestingly , the impact of protein motions on catalysis 
 is larger in ecdhfr - n23pp / s148a , previously called a  dynamic 
 knockout enzyme , than in the 
 wild type , as reflected in the smaller value of the recrossing transmission 
 coefficient and the increased value of k / k for ecdhfr - n23pp / s148a relative 
 to ecdhfr . simulations that explicitly consider the changes in the 
 environment during the chemical step show that the variant enzyme 
 is less well set up to accommodate the chemical reaction and thus 
 a higher degree of reorganization is required to go from the rs to 
 the ts . this effect provokes a larger participation of protein motions 
 in the reaction coordinate , as reflected in the smaller value of the 
 transmission coefficient . although millisecond conformational fluctuations 
 in the active site of ecdhfr are lost in the n23pp / s148a variant , these motions are not directly relevant to hydride 
 transfer , as demonstrated by our characterization of the solvent coordinate 
 changes during the chemical step . in fact , at the ts , the mobility 
 of active site residues on the fs ps time scale is slightly 
 larger in ecdhfr - n23pp / s148a than in the wild type . unlike in other 
 enzymes , where motions on one time scale may promote those on another , the n23pp / s148a mutation has very different effects on protein motions 
 depending on the time scale . motions on the s  ms time 
 scale are lost ( at least in the m20 loop ) , those on the ps  ns time scale are unaffected , while those on the fs ecdhfr - n23pp / s148a is therefore only a dynamic 
 knockout on the time scale typical for conformational motions , but 
 it is a  dynamic knock - in  at the level of the chemical 
 step . the increased dynamic coupling of enzyme motions to the chemical 
 coordinate is in fact detrimental to catalysis . our findings most 
 likely also apply to other enzyme - catalyzed reactions , although further 
 studies are required to identify the nature of the motions that contribute 
 to the recrossing coefficient in each case before predictive general 
 conclusions can be drawn .
isotopic 
 substitution ( 15n , 13c , 2h ) of a 
 catalytically compromised variant of escherichia 
 coli dihydrofolate reductase , ecdhfr - n23pp / s148a , has been 
 used to investigate the effect of these mutations on catalysis . 
 the 
 reduction of the rate constant of the chemical step in the ecdhfr - n23pp / s148a 
 catalyzed reaction is essentially a consequence of an increase of 
 the quasi - classical free energy barrier and to a minor extent of an 
 increased number of recrossing trajectories on the transition state 
 dividing surface . 
 since the variant enzyme is less well set up to 
 catalyze the reaction , a higher degree of active site reorganization 
 is needed to reach the ts . although millisecond active site motions 
 are lost in the variant , there is greater flexibility on the femtosecond 
 time scale . 
 the  dynamic knockout  ecdhfr - n23pp / s148a 
 is therefore a  dynamic knock - in  at the level of the 
 chemical step , and the increased dynamic coupling to the chemical 
 coordinate is in fact detrimental to catalysis . 
 this finding is most 
 likely applicable not just to hydrogen transfer in ecdhfr but also 
 to other enzymatic systems .