enzymatic catalysis , defined as the degree 
 to which an enzyme is 
 able to accelerate the rate of a given chemical reaction , remains to be fully understood . enzymes are able 
 to achieve rate enhancements in the range of 1010 in comparison to uncatalyzed reactions , exceeding those of any artificial catalysts by many orders 
 of magnitude . since the theory of transition 
 state stabilization was introduced by linus pauling , enzymatic catalysis has been historically defined in terms 
 of the ability of an enzyme to accommodate the electrostatic and geometric 
 configuration of a chemical transition state . according to this theory , the rate enhancement of an enzyme - catalyzed 
 reaction is proportional to the free energy difference between the 
 enzymatic and unbound transition state , which is of course a truism . the real question is what is the physical 
 origin of that free energy difference . over the course of an 
 enzymatic cycle , the protein bulk of an enzyme 
 can sample a myriad of conformations resulting 
 in a complex hierarchy of dynamic transitions over a wide range of 
 time scales . one of the most widely studied 
 enzymes with regard to the impact of protein dynamics on catalysis 
 occurring on a time scale of microseconds to milliseconds is dihydrofolate 
 reductase ( dhfr ) . this enzyme is essential for 
 maintenance of the proper intracellular concentration of tetrahydrofolate , 
 a coenzyme involved in the biosynthesis of purines , pyrimidines , and 
 some amino acids . dhfr catalyzes the 
 reduction of dihydrofolate to tetrahydrofolate via a protonation step 
 and a hydride transfer . protonation of the n5 atom of dihydrofolate 
 occurs by way of solvent exchange , whereas hydride transfer from the 
 nicotinamide ring of the cofactor nicotinamide adenine dinucleotide 
 phosphate ( nadph ) to the c6 position of the substrate is directly 
 catalyzed by the enzyme . in escherichia coli dhfr ( ecdhfr ) , the hydride 
 transfer step is mediated by thermally averaged equilibrium fluctuations 
 of the enzyme that result in a small population 
 of reactive conformations . several evolutionarily 
 conserved residues distal from the active site of ecdhfr have been 
 implicated as key loci in the motions allowing for hydride transfer . mutation of these residues leads to a decrease 
 in the catalytic rate by altering the probabilistic sampling of distinct 
 enzymatic conformations . these ecdhfr 
 motions are slow compared to the time scale of chemical transformation 
 ( femtoseconds ) , and thus can only impact the catalyzed reaction in 
 a statistical manner . in contrast , it 
 is possible that protein dynamics occurring on the femtosecond time 
 scale , which is the same time scale as chemical bond vibrations , can 
 dynamically couple to enzymatic barrier crossing . in this manuscript , we will show that this 
 is obtained in human dhfr ( hsdhfr ) . these fast protein motions , 
 termed promoting vibrations ( pvs ) , 
 are types of nonequilibrium density fluctuations that propagate through 
 specific structures within a protein . these motions act to dynamically modulate both the width and height 
 of the chemical barrier , resulting in an increase in reaction rate . although pvs have been identified in the reaction coordinates of 
 several enzymes , fast enzyme dynamics have been shown to have no effect on hydride 
 transfer catalyzed by ecdhfr . furthermore , 
 the network of coupled protein dynamics of ecdhfr is incapable of 
 sustaining dynamic correlations between fast vibrational motions at 
 distances greater than 46  . this characteristic of the dynamic landscape of ecdhfr obviates 
 the possibility of the incorporation of fast motions of the protein 
 bulk in the ecdhfr reaction coordinate , and previous work in our group confirms the absence of a pv in this 
 enzyme . recently , interest has 
 developed regarding the question of how 
 evolution has altered the catalytic and dynamic properties of dhfr . a study of hsdhfr conducted by wright and co - workers revealed that 
 the human enzyme exhibits a dynamic landscape that is highly divergent 
 from that of ecdhfr . this effect was 
 primarily observed in the dynamics of specific mobile loops of the 
 enzyme , which exhibit smaller scale fluctuations in hsdhfr compared 
 to those in ecdhfr , which is due to increased flexibility resulting 
 from the incorporation of additional residues . accompanying this change 
 in dynamic landscape in the human enzyme is tighter active site packing . 
 in hsdhfr , ligand flux is mediated by a twisting - hinge motion of the 
 met20 domain , whereas the opening and closing of the met20 loop modulates 
 ligand binding and unbinding in ecdhfr . the human enzyme also lacks 
 conformational changes that differentiate the michaelis complex and 
 the product ternary complex in prokaryotic forms of dhfr , including 
 ecdhfr . because hsdhfr is approximately 10 times more susceptible 
 to end - product inhibition , the authors conclude that the evolution 
 of a new dynamic mechanism in hsdhfr might be an adaptation in response 
 to the disparate relative concentrations of nadph in relation to nadp that is observed in vertebrate versus prokaryotic cells ( 100:1 
 ratio in humans and 1:1 in e. coli ) . another relevant study conducted by liu et al . showed 
 that specific 
 mutations along the evolutionary path from esdhfr to hsdhfr , also 
 known as phylogenetically coherent events ( pces ) , affect the binding 
 properties and catalytic efficiency of the enzyme . the locations of the pces discussed in this paper are shown 
 in figure 1 for the hsdhfr system along with 
 a sequence alignment comparing the human and e. coli enzymes . the most recent of these pces , a pwpp modification of the 
 met20 region ( 21-pwnlpadl-27 in ecdhfr and 24-pwpplrne-31 in hsdhfr ) , 
 prevents this loop from assuming an open conformation in the human 
 enzyme and negatively impacts the catalytic rate when expressed individually 
 in an e. coli chimera enzyme . mutating two additional 
 pce regions ( ecdhfr g51 to hsdhfr 62-pekn-65 and a single l28f mutation ) 
 to humanlike sequences in an e. coli variant rectified 
 the pwpp catalytic deficit , and the end 
 result is a measurable improvement in catalytic efficiency in hsdhfr 
 compared to that of ecdhfr . considering the altered dynamic 
 landscape of hsdhfr in combination 
 with the effects of specific mutational events on dhfr catalysis , 
 our group hypothesized that fast protein dynamics might be dynamically 
 coupled to hsdhfr - catalyzed hydride transfer . in this work , we present 
 the results of a transition path sampling ( tps ) study indicating the presence of a pv in the reaction coordinate 
 of hsdhfr . the advantage of tps is that it is completely unbiased , 
 unlike other sampling methodologies such as umbrella sampling . it 
 is also entirely rigorous , with the only approximations being the 
 use of quantum mechanical / molecular mechanical ( qm / mm ) simulations 
 and semiempirical treatment of the quantum region . we stress that 
 the trajectories found via tps are classical in nature ; in other words , 
 they do not include the effects of hydride tunneling or zero point 
 energy . first , the promoting vibration , by compressing the 
 donor and acceptor , causes the barrier to be both lower and thinner . second , for other hydride 
 transfer enzymes , and alcohol dehydrogenase in particular , there is 
 some indication that tunneling plays a small role . michaelis complex of hsdhfr showing the locations of the putative 
 pv residues and a sequence alignment for the human and e. 
 coli enzymes . the bound ligands are cyan , the hydride donor is blue , 
 and the hydride acceptor is red . pv residues are depicted as follows : 
 i17 = green , f35 = orange , 24-pwpplrne-31 of the met20 loop = yellow , 
 f32 = violet , and 62-pekn-65 = magenta . regarding pces , the pwpp modification overlaps 
 with the yellow residues ; 24-pwpplrne-31 , 62-pekn-65 ( magenta ) , and 
 l28f ( violet ) mutational events are shown explicitly . to carry out the specific analyses discussed throughout 
 this paper , 
 we first generated a transition path ensemble ( tpe ) for the hsdhfr 
 hydride transfer reaction consisting of 200 individual reactive trajectories . we produced these trajectories via a microcanonical tps algorithm 
 adapted for the study of enzymatic reactions that maintains an acceptance ratio of 25% . to obtain a transition 
 state ensemble ( tse ) , or a set of atomic coordinates along the stochastic 
 separatrix , we calculated the commitment 
 probability of every 10th trajectory in the hsdhfr tpe . we considered 
 the time of barrier crossing to correspond to the time necessary for 
 the committor to rise from 0.1 to 0.9 , and we regarded the transition 
 state of each trajectory to be the time slice with a committor value 
 closest to 0.5 . for comparison purposes , we also utilized an ecdhfr 
 tpe and tse calculated previously . we performed all steps for system 
 setup using the program charmm unless otherwise noted . 
 to obtain initial atomic coordinates , we utilized the crystal structure 
 of human dhfr in a ternary complex with the cofactors nadph and folic 
 acid , which is a substrate mimic . this structure was solved to a resolution 
 of 1.20  by wright et al . ( pdb code 4m6k ) . to create 
 a reactive complex to study hydride transfer using the coordinates 
 of folic acid , we changed the protonation states of n1 , n8 , and protonated 
 c6 and generated atomistic parameters for this new ligand using the 
 program discoverystudio25 . also using this program , we added c - terminal 
 residues met1gly3 , which were not resolved in the original 
 crystal structure . we employed protonation states of all acidic and 
 basic amino acids corresponding to said state at physiological ph 
 as determined by charmm . to ready the complex for qm / mm simulation , 
 we isolated the quantum mechanical region ( the dihydronicotinamide 
 and ribose group of nadph and the majority of dihydrofolate , excluding 
 the glutamate tail ) as a separate residue , patched the boundary atoms 
 to the classical regions using the command pres , and constructed a 
 distinct parameter file for this new residue . for this new residue , 
 we used a nonstandard potential first calculated by garcia - viloca 
 et al . following this step , we solvated 
 the entire complex with an 85  - diameter sphere of tip3 water 
 models , incorporated all crystallographic 
 waters as tip3 models , and neutralized the charge of the system with 
 four potassium ions . we conducted all molecular dynamics ( md ) 
 and qm / mm simulations presented in this work using version 35 of the 
 program charmm . for classical simulations , we 
 implemented the charmm27 all - atom force field . during qm / mm , we simulated 
 the quantum region using the am1 potential and treated the boundary atoms using the generalized hybrid orbital 
 ( gho ) method . we conducted all integrations 
 of forces for md or qm / mm using time steps of 1 fs . the protocol we 
 utilized to minimize , heat , and equilibrate the hsdhfr system was 
 selected to mimic that implemented in our previous study on ecdhfr . for minimization , we first constrained all atoms 
 except tip3p waters and potassium ions using a harmonic potential 
 of 100 kcal mol  and 
 performed 100 steps of steepest descent ( sd ) followed by 100 steps 
 of the adopted basis newton  raphson method ( abnr ) . next , we 
 constrained only the protein and ligand atoms with 100 kcal mol  of harmonic force and 
 conducted 100 steps of abnr . next , we performed iterative minimization 
 cycles with the protein and ligand atoms constrained using force constants 
 of 75 , 50 , and 25 kcal mol  , successively . then , we conducted an unconstrained minimization 
 using qm / mm for 100 steps of abnr . to heat the system from 0 to 300 
 k , we incrementally added kinetic energy for a total of 30 ps while 
 implementing decreasing constraint levels in the same manner as the 
 described minimization protocol . using qm / mm , we equilibrated the 
 system at 300 k for 500 ps with zero applied constraints . we designated the initial 
 and final states of the reaction by implementing the following order 
 parameters : chemical species of the enzymatic reaction with a hydride acceptor 
 distance greater than or equal to 1.5  were considered part 
 of the reactant ( dihydrofolate ) basin , whereas species with a hydride  donor 
 distance greater than or equal to 1.5  and a hydride acceptor 
 distance less than or equal to 1.5  were designated as part 
 of the product ( tetrahydrofolate ) basin . following the next step of 
 the tps algorithm , we connected the reactant and product basins via 
 an initial , biased qm / mm trajectory of 250 fs for implementation of 
 the charmm command resd with the parameter that the hydride  acceptor 
 distance was constrained to 1.25  by a harmonic force constant 
 of 60 kcal mol  . using this initial constrained trajectory , we selected a random point 
 of integration , or time slice , along the trajectory and perturbed 
 the momentum of each atom in the system by adding a random value as 
 determined by selection from a zero - mean gaussian distribution multiplied 
 by a scaling factor of 0.2 . after rescaling these new momenta to conserve 
 total energy and eliminate any net angular or linear momenta , we propagated 
 the system both forward and backward for 250 fs in time to generate 
 a resultant trajectory of 500 fs in total length . we utilized this 
 process of randomly , iteratively perturbed time slices until we achieved 
 an ensemble of 230 reactive or qm / mm trajectories that connected both 
 designated configuration basins . we maintained a ratio of reactive 
 to nonreactive trajectories ( acceptance ratio ) of approximately 25% . 
 to ensure complete decorrelation from the original constrained reactive 
 trajectory , we disregarded the first 30 generated trajectories in 
 all of our analyses . to determine 
 the commitment 
 probability of a specific set of coordinates 
 corresponding to a particular time slice along a reactive trajectory , 
 we reinitialized the qm / mm dynamics at this point using random velocities 
 derived from a boltzmann distribution . all committors for individual 
 time slices were calculated using 50 trajectories of 250 fs each . we considered the value of the number of these trajectories landing 
 in the product basin divided by the total number of trajectories generated 
 to be representative of the committor value of the time slice . in 
 this respect , a point with a committor value of 1 would have a 100% 
 chance of reaching the product basin , whereas a set of atomic coordinates 
 and velocities with a committor of 0.5 would be equivalent to the 
 transition state . to determine the level to which a specific 
 degree of freedom was necessary for the transition state formation 
 of the enzymatic reactions of hsdhfr and ecdhfr , we conducted committor 
 distribution analyses . using a transition state as the 
 starting point , we conducted qm / mm simulations for a trajectory 1 
 ps in length while constraining the atoms of interest with a harmonic 
 force constant of 2000 kcal mol  . for all constraints relevant to the atoms of the protein , we constrained 
 with regard to both the hydride donor and acceptor and the -carbon 
 of the specific residues ( -carbon in the case of glycine ) . we calculated the committor value for every 50th slice of this constrained 
 trajectory , giving 20 committor values for each transition state . 
 for each committor distribution presented in this study , we used three 
 transition states as starter points . in principal component 
 analysis ( pca ) , one must first determine the eigenvectors of the correlation 
 matrix of the data ; then , the variance of the data along these eigenvectors 
 is proportional to the corresponding eigenvalues . if the eigenvalues 
 of the first few eigenvectors are dominant , then they form a low - dimensional 
 representation of the data . the limitation of pca is that it implicitly 
 linearizes data , which is not a good approximation for the distribution 
 of transition states on the separatrix . to correct for the linearization 
 assumption , we used kernel pca ( kpca ) . in kpca , a nonlinear transformation 
 of the original data is made to a space where the pca is valid , pca 
 is performed there , and then the results are transformed back to the 
 original space . we found that quadratic polynomial transformation 
 ( xy ) led to the first 
 eigenvector dominating the variance . the direction of the reaction 
 coordinate is perpendicular to the separatrix ; therefore , we found 
 the residues that contributed the least to this dominant 
 eigenvector . notably , all calculation methods and 
 parameters reproduced the data from our original ecdhfr study to ensure 
 that direct comparisons are appropriate . we utilized 
 committor distribution analysis to study the reaction 
 coordinate of hsdhfr in comparison with that 
 of ecdhfr . committor distribution for an enzyme - catalyzed reaction 
 is a rigorous computational method that is utilized to deduce the 
 complete enzymatic reaction coordinate . the first step in this 
 analysis is to use the coordinates of an extant transition state to 
 initiate a constrained qm / mm trajectory . if the correct set of reaction 
 coordinate variables is constrained , the resultant trajectory will 
 remain on the separatrix . the next step is to run committor analysis 
 using points along this new constrained trajectory to obtain a distribution 
 of committor values . a correct selection of relevant degrees of freedom 
 would yield a distribution peak at 0.5 . because of the complexity 
 of the enzymatic reactions and the statistical nature of the calculation , 
 it is expected that selection of an accurate enzymatic reaction coordinate 
 will yield a broad distribution centered at 0.5 . incorrect selections 
 of the reaction coordinate in an enzymatic system will generally result 
 in distributions with a peak far from the 0.5 committor value . using this analysis , we found that a subpicosecond protein 
 motion is dynamically coupled to the reaction catalyzed by hsdhfr . committor distribution analysis is used to determine what motions 
 are on the dividing surface ( the stochastic separatrix ) , and what 
 motions are orthogonal to it . the term dynamic coupling refers to 
 degrees of freedom that are part of the reaction coordinate and occur 
 on the same time scale as barrier passage . in other words , the promoting 
 vibration modulates the barrier and does so on a time scale that is 
 comparable to passage over the barrier ( i.e. , they are not adiabatically 
 separable ) . we observed that the minimal definition of the hsdhfr 
 reaction 
 coordinate required the inclusion of the positions of the following 
 residues : i17 , 24-pwpplrne-31 , f32 , f35 , and 62-pekn-65 ( figure 1 ) . the residues 24-pwpplrne-31 include the pwpp 
 modification of the met20 loop ; f32 and 62-pekn-65 also correspond 
 to previously reported pces in the dhfr protein family . evolutionarily analogous residues in ecdhfr 
 ( i14 , 21-pwnlpad-27 , f31 , and g51 ) were not part of the ecdhfr reaction 
 coordinate . figure 2 shows select committor 
 distributions generated for both the hsdhfr and ecdhfr systems . to 
 create each distribution , we utilized three transition states as starting 
 points for the production of three constrained qm / mm trajectories 
 1 ps in length . we performed committor analysis on every 50th time 
 slice of each new trajectory to obtain a set of committor values . we performed calculations while implementing constraints on the following 
 variables : ( 1 ) the hydride  donor and hydride acceptor 
 distances ( ecdhfr , figure 2a ; hsdhfr , figure 2d ) , ( 2 ) the positions of the atoms for nadph and 
 dihydrofolate ligands ( ecdhfr , figure 2b ; hsdhfr , 
 figure 2e ) , and ( 3 ) the positions of the ligand 
 atoms in addition to the distances between the -carbons ( -carbon 
 in the case of glycine ) of the putative pv residues and the hydride 
 donor and acceptor ( ecdhfr , figure 2c ; hsdhfr , 
 figure 2e ) . histograms of committor distributions 
 obtained with increasing 
 numbers of constraints for the ecdhfr and hsdhfr systems . graphs ( a ) , 
 ( b ) , and ( c ) correspond to ecdhfr , whereas ( d ) , ( e ) , and ( f ) pertain 
 to the hsdhfr system . data shown in ( a ) and ( d ) were obtained while 
 constraining only the distances between the hydride and the donor 
 and acceptor , ( b ) and ( e ) illustrate the results of the committor 
 distribution calculation while applying constraints to all atoms of 
 the ligands , and ( c ) and ( f ) represent data derived while constraining 
 the residues of the putative pv ( i14 , 21-pwnlpad-27 , f31 , and g51 
 in ecdhfr ; i17 , 24-pwpplrne-31 , f32 , f35 , and 62-pekn-65 in hsdhfr ) . in the hsdhfr system , increasing 
 the number of constraints resulted 
 in a committor distribution that peaked close to 0.5 . additionally , 
 the incorporation of protein constraints was essential for achieving 
 an adequate description of the hsdhfr enzymatic reaction coordinate . all of the distributions calculated for ecdhfr are centered far from 
 0.5 , demonstrating that the constraints tested were not sufficient 
 approximations of the enzymatic reaction coordinate . when only the 
 atomic positions of the ligands were constrained , hsdhfr exhibited 
 a marked improvement in the centering of the committor distribution , 
 whereas ecdhfr did not . because the ligands interact with a large 
 portion of the protein in both dhfr systems , it is likely that constraining 
 these atoms resulted in a general constraint on protein conformation . the gradual transition to a distribution that peaked closer to 0.5 
 suggests that the reaction coordinate in the hsdhfr system is a wider 
 tube in configuration space ( i.e. , in protein structure ) . it must 
 be reiterated that these differences are qualitative ; however , it 
 is clear that there are basic physical differences captured by the 
 variation between panels c and f of figure 2 . it is also possible that there is a set of protein constraints 
 that would imply direct coupling of ecdhfr protein motions to hydride 
 transfer , but given the preponderance of evidence , that seems highly 
 unlikely . we observed an increase in structural 
 variation of the transition states in the tse of hsdhfr when compared 
 to those sampled by ecdhfr . first , we calculated the rmsd values for 
 the position of only the ligand atoms at each transition state versus 
 those of the average transition state to be 0.0779 and 0.221  
 in ecdhfr and hsdhfr , respectively . we then used the atomistic structures 
 of the transition state conformations of the protein to perform this 
 calculation and obtained rmsd values of 0.0594 and 0.154  for 
 the transition state conformations of ecdhfr and hsdhfr , respectively . acceptor 
 angle at the transition state in hsdhfr compared to that of ecdhfr . 
 although the average value for this angle was similar for both enzymatic 
 systems ( 151.92 and 151.00 in ecdhfr and hsdhfr , respectively ) , 
 the standard deviation for this angle was greater in the human enzyme 
 ( 3.2 and 73 in ecdhfr and hsdhfr , respectively ) . it is 
 important to note that these rmsd values must be considered qualitative 
 measures of transition state variation . we also detected increased 
 variability in the times of barrier crossing for the hsdhfr tpe in 
 comparison to those calculated for the ecdhfr tpe . figure 3a shows box plots representing the distributions 
 of barrier crossing times exhibited by both the ecdhfr and hsdhfr 
 systems . in ecdhfr , the distribution of committors calculated has 
 a breadth of only 2 fs , whereas the corresponding distribution for 
 the hsdhfr system spans 17 fs . these distribution differences are 
 associated with a p value of less than or equal to 
 0.05 . this result may be indicative of an increase in the ruggedness 
 of the free energy landscape of the hsdhfr reaction compared to that 
 of the reaction catalyzed by ecdhfr . the e. coli enzyme 
 is clearly a much stronger funnel to a single path through the reactive 
 phase space . these results demonstrate that the evolutionary changes 
 allow for greater variation in paths through the reactive phase space 
 in hsdhfr compared to that of the prokaryotic enzyme . although it 
 is unclear what exactly this may confer biologically , the physical 
 observation is definitive . we can only speculate that this greater 
 chemical path flexibility may allow for greater responsiveness to 
 the variable chemical environments found in eukaryotic systems . ( a ) box plots illustrating the differences in the distributions 
 of barrier crossing times for the ecdhfr tpe ( ectpe ) and hsdhfr tpe 
 ( hstpe ) . each distribution was calculated using barrier crossing times 
 from 21 representative trajectories in each tpe . for the ectpe , the 
 shortest and longest times of barrier crossing were 1 and 3 fs , respectively . the values for the 2nd quartile , median , and 4th quartile were all 
 2 fs . in the hstpe , the corresponding values were as follows : shortest 
 time = 2 fs , 2nd quartile = 4 fs , median = 6 fs , 4th quartile = 8 
 fs , and the longest time = 18 fs . ( b ) kpca calculation for the ecdhfr 
 tse , with putative pv residues at positions 14 , 2127 , 31 , 
 and 51 indicated with red circles . ( c ) kpca calculation for the hsdhfr 
 tse , with putative pv residues at positions 17 , 2431 , 35 , 
 and 6265 indicated with red circles . to determine the contribution of the position of each residue 
 to 
 the variance in the hsdhfr and ecdhfr tses , we conducted kernel principal 
 component analysis . this technique presents 
 a way to perform orthogonal transformation of a multidimensional surface , 
 such as tse , through nonlinear kernels . we have previously used this 
 technique as a way to identify pv residues in the enzymatic reaction 
 coordinate of human heart lactate dehydrogenase ( ldh ) . in ldh , the residues contributing the least 
 to the first principal component ( pc ) were able to adequately approximate 
 the enzymatic reaction coordinate . the results of this calculation 
 for the ecdhfr tpe and hsdhfr tpe are displayed in figure 3b and 3c , respectively . the 
 residues of the putative pv are highlighted with red circles ( i14 , 
 21-pwnlpad-27 , f31 , and g51 in ecdhfr ; i17 , 24-pwpplrne-31 , f32 , f35 , 
 and 62-pekn-65 in hsdhfr ) . in hsdhfr , all but two of the pv residues 
 corresponded to minima along the first pc , whereas the majority of 
 these residues in ecdhfr did not . we found that a compressive 
 motion between residues i17 and p35 
 correlates with a dynamic decrease in the hydride donor acceptor 
 distance and with the time of barrier crossing in the hsdhfr system . figure 4 shows the time series representing 
 specific dynamic distances during an exemplary trajectory along with 
 the moment of chemical barrier passage ( gray region : 354361 
 fs ) . breaking of the hydride  donor bond ( red ) and formation 
 of the hydride  acceptor bond ( blue ) are shown in figure 4a along with the donor figure 4b is a 
 representation of specific distances between different aspects of 
 the protein during the same example trajectory . the compression between 
 i17 and p35 ( orange ) coincides with a smaller compressive fluctuation 
 between i17 and the hydride acceptor ( violet ) following an excursion 
 of p24 toward i17 ( green ) . this fast motion of p24 toward i17 is the 
 result of a density fluctuation propagating through the protein bulk , 
 which was also the case for the previously identified pv in the reaction 
 coordinate of human heart lactate dehydrogenase . distance time series of an exemplary reactive trajectory illustrating 
 the dynamic contributions of specific residues to chemical barrier 
 passage in hsdhfr . ( a ) distances corresponding to the chemical reaction 
 ( red = hydride  acceptor , blue = hydride  donor , and black 
 = donor  acceptor ) . ( b ) dynamic distances within the protein 
 ( orange = i17(atom he1)f35(atom hd1 ) , violet = i17(atom cb)acceptor , 
 and green = p24(atom cb)i17(atom cb ) ) . the gray region represents 
 the time of barrier passage for this specific trajectory ( 354361 
 fs ) . we detected subtle structural 
 changes between the active sites 
 of ecdhfr and hsdhfr , which establish a physical link between the 
 hydride donor  acceptor axis and the pv residues in hsdhfr . figure 5 shows the position of pv residues 
 near the active site in relation to the hydride donor the hinges of the met20 
 loop , p24 and g31 , come into direct contact with i17 and f35 , respectively , 
 and these two amino acids are ideally situated on either end of the 
 hydride donor  acceptor axis . the active site of ecdhfr is too 
 loosely packed to support these specific contacts . in particular , 
 the close van der waals interaction between i17 and p24 in hsdhfr 
 is not pronounced in the analogous residues of ecdhfr ( i14 and p21 ) . tighter packing of the hsdhfr active site may be an important enabling 
 factor for the incorporation of fast protein dynamics in the hsdhfr 
 reaction coordinate . view of the equilibrated structure of the ( a ) ecdhfr and ( b ) hsdhfr 
 system . the ligands are cyan , the hydrides are violet , the hydride 
 donors are blue , and the hydride acceptors are red . residues of the 
 met20 loop are yellow , i14/17 is green , and residue f31/35 is orange . the 
 committor distribution analysis data presented here represent 
 our best attempt at isolating the reaction coordinate of hsdhfr . we 
 tried many combinations of candidate residues based on the kpca output . 
 incorporating residues that also corresponded to important mutational 
 events was key to our elucidation of the reaction we show 
 that the subpicosecond protein motion in a specific set 
 of residues is dynamically coupled to the reaction coordinate of hsdhfr . contradistinctively , there is no indication 
 of a pv in the enzymatic reaction coordinate of ecdhfr , suggesting 
 a change in the form of catalysis from the e. coli to human enzyme . it could be possible to experimentally validate 
 this finding through kinetic studies of enzymes that are expressed 
 utilizing heavy - isotope substitution throughout the protein matrix . if a pv is in fact dynamically coupled to the 
 enzymatic reaction coordinate , a heavy  enzyme would 
 exhibit a decreased probability of barrier crossing , which would not 
 be the case if there was no such coupling . experimental and theoretical evidence indicates that the enzymatic rate enhancement 
 of ecdhfr is primarily governed by electrostatic effects , but electrostatics 
 do not appear to be the sole factor responsible for catalysis in hsdhfr . 
 as one of the key mutations differentiating ecdhfr from hsdhfr , pwpp 
 modification of the met20 loop has been implicated in electrostatic 
 stabilization of the transition state for the ecdhfr - catalyzed hydride 
 transfer reaction , and the presence of 
 this modification in a chimera e. coli enzyme results 
 in a decreased hydride transfer rate . concurrent with this modification hindering the electrostatic - based 
 catalysis of ecdhfr , this mutational event also led to a change in 
 the conformational states of hsdhfr and a more tightly packed active 
 site . combined with the other mutational events 
 that separate the e. coli and human enzymes , this 
 alteration of the met20 loop allows for a mechanism of catalysis in 
 the hsdhfr that includes rapid protein dynamics or a pv . we 
 also found that the stochastic separatrix , or tpe , of the ecdhfr - catalyzed 
 reaction is more narrow in terms of the geometry of the transition 
 state structures and the variability of reactive conformations as 
 compared to the enzymatic reaction of hsdhfr . this finding is in agreement 
 with our committor distribution results demonstrating a smaller degree 
 of tolerance for changes in the enzymatic conformation of ecdhfr relative 
 to hsdhfr in order to remain on the separatrix . our inability to identify 
 a definitive reaction coordinate for the ecdhfr - catalyzed reaction 
 also indicates that perturbation of the ecdhfr transition state structure 
 is more likely to result in deviation from the separatrix compared 
 to doing so with the human enzyme . when considered within the context 
 of the conformational landscape model of enzymatic reactions , these results suggest that fast 
 distance sampling along the reaction coordinate indicative of a pv 
 could introduce a degree of finely grained ruggedness to the free 
 energy landscape of an enzymatic reaction . thus , it can be argued 
 that dynamic coupling of protein motion to the reaction coordinate 
 increases the likelihood of barrier crossing by decreasing the need 
 for an optimal electrostatic and geometric arrangement of the active 
 site . as an extension of this conclusion , the breadth of possible 
 reactive conformations corresponding to a specific conformational 
 basin appears to be greater for the hsdhfr enzymatic system than for 
 the ecdhfr system . an almost philosophical question relates 
 to the selective pressure 
 that caused such exquisite design of active sites when the chemistry 
 is almost never rate limiting . this is a conundrum for enzymatic active 
 sites in general , not just promoting vibrations . the results of this 
 study indicate that possible selective pressure on the protein matrix , 
 which was likely optimized after a static active site , was robustness 
 to multiple phase space paths rather than optimization of the chemical 
 rate , although this is purely speculation . further work is needed 
 to elucidate possible evolutionary pressures for enzymatic promoting 
 vibrations .