while the importance 
 of protein conformational heterogeneity and 
 dynamics in enzymatic catalysis is well established , it has been difficult 
 to observe their influence directly . the fluctuation 
 of protein structures is implicit to modern descriptions of catalytic 
 function ranging from preorganization of the active site to induced 
 fit . conformational equilibria that occur on the nanosecond to millisecond 
 time scale are of particular interest because they perturb average 
 values of reactive structures , such as the donor acceptor distance 
 for hydride transfer , and thereby modulate the catalytic rate . despite the importance of these concepts , the most widely used approach 
 to analyze enzyme kinetics in the literature and textbooks still relies 
 on the michaelis  menten model and transition state theory . this approach has served its purpose as an organizing framework for 
 interpreting enzyme kinetics , but it tends to oversimplify enzyme 
 reaction pathways . transition state theory further 
 develops this concept by postulating a single barrier to proceeding 
 from the michaelis state to the product state and thus a single transition 
 state that dictates enzyme selectivity and function . together they describe a single pathway for catalytic competency 
 with only a few populated structures . however , it has long been recognized 
 that proteins , and enzymes specifically , do not exist in unique three - dimensional 
 conformations . instead , proteins are best described in a hierarchy 
 of interconnected conformations or substates . the existence of such substates suggests that the progress of an 
 enzymatic reaction from reactive conformations is substantially more 
 complicated than transition state theory would have it . we have studied the 
 role of conformational heterogeneity and dynamics 
 in the catalysis of hydride transfer by the enzyme lactate dehydrogenase 
 from pig heart ( phldh ) . this enzyme catalyzes the reduction of pyruvate 
 to lactate mediated by the transfer of a hydride from nadh to c-2 
 of pyruvate , as shown in figure 1 . the phldh reaction 
 is rigorously ordered : nadh binds first , followed by pyruvate and 
 then the on - enzyme chemistry . the catalytic 
 mechanism has been well - studied previously with various methods . finally , the system may be prepared such that , at equilibrium , half 
 occupies the pyruvate side of the reaction and half the lactate side . hence , the actual michaelis complex may be studied 
 without resorting to the use of substrate mimics . schematic of the ldh 
 active site showing the residues stabilizing 
 the substrate pyruvate and the proximity of the cofactor , nadh . the catalytically key surface loop ( residues 98110 ) closes 
 over the active site , bringing residue arg109 in hydrogen bond contact 
 with the ligand , forcing water to leave the pocket , and , accompanied 
 by the motions of mobile areas in the protein , rearranges the pocket 
 geometry to allow for favorable interactions between the cofactor 
 and the ligand that facilitate on - enzyme catalysis . of particular 
 interest to this work are the hydrogen bonds formed between arg-109 
 and his-195 to the c2 carbonyl of pyruvate ( emphasized in red ) . we have previously reported on 
 the existence of a heterogeneous 
 population of phldh - bound pyruvate substates while at equilibrium . our previous work observed this heterogeneity 
 using isotope - edited difference ftir methods to detect multiple c-2 
 pyruvate carbonyl stretches characteristic of enzyme - bound substrate 
 that are present simultaneously at equilibrium . heterogeneity at the 
 c-2 carbonyl of pyruvate is particularly relevant to questions about 
 catalysis in ldh because it has been previously shown that the electrostatic 
 interactions between this carbonyl and the protein residues his195 
 and arg109 are responsible for as much as a 10 catalytic 
 rate enhancement of the overall 10 enhancement from the 
 enzyme . the equilibrium difference infrared 
 spectrum was resolved into four unique bands characteristic of enzyme - bound 
 pyruvate at 1674 , 1679 , 1686 , and 1703 cm as compared 
 to free pyruvate at 1710 cm . these four bands 
 are direct evidence of the multiple available conformations in the 
 michaelis complex but do not report on the reactivity or catalytic 
 relevance of any of the observed substates . here we present a study 
 of the catalytic relevance of these substates by observing the relaxation 
 kinetics of each substate using temperature - jump infrared ( t - jump 
 ir ) spectroscopy . we then present a scheme for the catalytic landscape 
 that incorporates each of these substates based on kinetic modeling 
 of the relaxation data . nad , nadh , and pig heart ldh 
 ( phldh ) were purchased from roche diagnostics ( indianapolis , in ) . 
 [ n]ammonium chloride , [ u - c]glucose , and 
 [ 2-c]pyruvate were purchased from cambridge isotope laboratories 
 ( tewksbury , ma ) . briefly , the phldh gene was obtained from zyagen s 
 ( san diego , ca ) pig heart cdna library . the gene and a six - residue 
 his tag were subcloned into pet14b plasmids from novagen ( merck kgaa , 
 darmstadt , germany ) and transformed into c43(de3 ) competent e. coli cells from overexpress ( imaxio , saint - beauzire , 
 france ) . the cells were grown in minimal media supplemented with the 
 labeled glucose and ammonium chloride indicated above . the resulting uniformly labeled protein 
 was purified in the same manner described for unlabeled phldh . all experiments described here , except where 
 noted , utilized [ u - n , -c]phldh and the resulting 
 uniformly labeled enzyme will be referred to simply as ldh . static ftir spectroscopy was carried 
 out on a magna 760 fourier transform spectrometer ( nicolet , instrument 
 corporation , madison , wi ) using an mct detector as described previously . spectra were collected in the range 11004000 
 cm with 2 cm resolution . a 
 blackman  harris three - term apodization and a happ all samples 
 were prepared in d2o buffer with 100 mm phosphate at ph 
 7.2 ( ph meter reading ) . the ldh reaction mixture was prepared at the 
 initial concentrations of 4:4:20 mm ( ldhnadlactate , 
 where ldh concentration refers to active sites ) . under such conditions , about half of the nad was converted to nadh , yielding 
 an on - enzyme pyruvate concentration of about 2 mm as determined by 
 uv  vis measurements . this high 
 protein concentration is required to observe the weak absorbance of 
 a single substrate carbonyl bond in the large enzyme complex , as each 
 protein active site only binds one substrate . we did not observe protein 
 aggregation at this concentration on the basis of the complete absence 
 of the intense ir marker bands for aggregation . additionally , we performed 
 temperature - dependent ftir measurements on this same reaction mixture . collection of spectra 
 and temperature control were automated by labview ( national instruments , 
 austin , tx ) routines written in our lab . briefly , a 1.91 m pump beam is produced by the first stokes 
 shift of the fundamental line from a nd : yag laser ( 30 mj / pulse , 10 
 hz repetition rate , 10 ns pulse width , spectra physics ( mountain view , 
 ca ) ) pumping a h2-filled raman shifter . the 1.91 m 
 pump beam is absorbed weakly by the combination bands of the d2o solution , allowing for near uniform heating of the solution . the heated region is probed by a quantum cascade laser ( daylight solutions 
 inc . , poway , ca ) tunable from 1565 to 1723 cm . changes in probe beam transmission are detected by a fast ( 200 mhz ) 
 photovoltaic mct detector ( kolmar technologies , newburyport , ma ) , 
 and the signal is filtered and amplified in a low noise preamplifier 
 ( sr560 , stanford research systems ) . typically , 10000 pump the sample 
 cell path length was 200 m . temperature jumps of 8 and 15 c 
 were employed in this study . a consistent final temperature of 30 
 c was used so that all results were reporting on the same thermal 
 equilibrium . the useful time range of the instrument used in this 
 study is from 10 s to 1 ms . the lower limit of this range is 
 set by the bandwidth of the preamplifier . the geometry of our cell 
 arrangement is such that heat diffuses out of the irradiated volume 
 with a lifetime of a few ms ; this determines the duration of the t - jump 
 and thus sets an upper limit to the useful time range . the relaxation 
 spectra of the enzyme complexes with infrared probes at pyruvate frequencies 
 contain signals not only from pyruvate but also from the protein , 
 because it has a broad background absorbance in this region . two types 
 of difference methods were used to remove the contributions from the 
 protein kinetics in these data . the first was to use the isotope edited 
 methods similar to that for the static infrared studies , as described 
 in detail in refs ( 25 , 29 , and 32 ) . in this approach , the pyruvate - specific 
 infrared probes were used on both enzyme complexes with cofactor / pyruvate 
 and with cofactor/[2-c]pyruvate . the contribution from 
 protein in the relaxation transient can be eliminated by subtraction 
 of the ir transient of the enzyme complex with [ 2-c]pyruvate 
 from the unlabeled complex . the second method is to use an infrared 
 probe that is off resonance from the pyruvate frequencies so that 
 only the background protein relaxation transient is obtained . in our 
 case , 1695 cm is used as a reference probe frequency , 
 since the static data indicate that the pyruvate c2=o stretch 
 mode is absent at this frequency . subtraction of the protein kinetics 
 from the data with infrared probes specific for pyruvate substates 
 yields the relaxation kinetics of only those substates . we have found 
 the kinetic results obtained by these two methods are very similar , 
 especially in the frequency region of the heterogeneous broadened 
 1680 cm band . modeling a proposed reaction scheme 
 to fit the measured temperature - jump kinetics was performed with matlab 
 2013b ( mathworks , natlick , ma ) using routines written in our lab . a standard curve fitting approach is not applicable to this problem 
 because there is not enough information known about the rate constants 
 at each step and such an approach would be underdetermined . instead , 
 our overall approach was to test how well the predicted relaxation 
 kinetics from an input reaction scheme match the experimental relaxation 
 ( temperature - jump ) results . this approach 
 necessitates a large number of variables to fully describe the system . the routine involves four main steps and requires an input reaction 
 scheme , a set of rate constants , and activation energies that define 
 the scheme at a given temperature , initial and final jump temperatures , 
 and initial concentrations of each component in the reaction scheme . step two determines equilibrium concentrations 
 of all states at each temperature using a master equation approach . step four calculates a time - dependent profile 
 of each state based on the parameters calculated in the previous steps . 
 to quantitatively compare similarity between a predicted set of results 
 and the experimental data , we devised a scoring method that considers 
 all of the transient data at five different probe frequencies . first , 
 we calculated an accuracy score for each transient , as shown in eq 11where j is each probe frequency , n is the total number 
 of points in the transient , and i is a given point 
 in time . this method gives a direct measure 
 of how accurately the predicted transient matches the experiment and 
 ignores whether the predicted data over- or underestimates the experimental 
 data . finally , a composite score for an entire 
 fitting run is compiled as the summation of all the transient scores , 
 as shown in eq 2.2 the total 
 score is used for comparison 
 as the whole process is cycled in a monte carlo fashion where a rate 
 constant is randomly modified , the steps are repeated , and the score 
 is computed to determine if the fit is improved . to test multiple 
 trajectories with many monte carlo steps in a reasonable amount of 
 time , the calculations were performed on a multiprocessor cluster 
 in the emerson center for scientific computation . figure 2 displays the 
 infrared isotope edited difference spectra of ldh - bound 
 pyruvate at 5 , 15 , 25 , and 35 c . the difference spectra were 
 generated by subtracting the protein - bound [ 2-c]pyruvate 
 spectra from the protein - bound [ 2-c]pyruvate spectra 
 at each temperature . the resulting difference spectra report only 
 on the infrared bands that are affected by the label ; therefore , these 
 ir difference features report directly on the reactive carbonyl bond 
 involved in the catalytic turnover . the [ 2-c]pyruvate 
 carbonyl stretches are the positive bands in the spectrum , whereas 
 the [ 2-c]pyruvate carbonyl stretches would appear as 
 negative bands at lower energy ; the negative bands are visible in 
 figure s1 ( supporting information ) . the 
 carbonyl infrared stretch overlaps with strong h2o absorption 
 bands and the amide i bands of the protein backbone . to minimize this 
 spectral overlap , we worked with d2o solutions of uniformly 
 isotope - labeled [ u - n , -c]ldh . the larger 
 molecular mass shifts the protein amide - i infrared absorbance to lower 
 energy , away from the pyruvate c2=o stretch frequency . isotope - labeled 
 difference ftir spectra of [ u - n , -c]ldhnadh[2-c]pyruvate minus 
 [ u - n , -c]ldhnadh[2-c]pyruvate at the indicated temperatures . the c2=o stretch ir spectrum 
 of bound pyruvate 
 is heterogeneously broadened . gaussian fits to the spectrum reveal 
 several sub - bands that we assign to different enzyme - bound pyruvate 
 conformational substates . a reasonable 
 fit of the data was produced by the sum of four gaussian sub - bands 
 with center frequencies at 1674 , 1679 , 1686 , and 1703 cm , although we can not rule out the possibility that each of these 
 bands could be composed of more than one overlapping substate . these 
 gaussian sub - bands are shown in figure s1 ( supporting 
 information ) . there is also the likelihood of sparsely populated 
 substates that are not apparent in the ir difference spectra due to 
 limited sensitivity . this indicates the population shifts away from bound pyruvate 
 either to free pyruvate or to the product side ( bound or free lactate ) 
 at higher temperature . the ir difference spectra do not allow us to 
 track the lactate population directly , because upon conversion to 
 lactate the c2 carbonyl infrared stretch is lost and the corresponding 
 lactate vibration is not observed in this spectral region ( it is at 
 lower frequency and obscured by protein absorbance ) . the second observation 
 is that a new equilibrium is established among the substates when 
 comparing the lowest temperature spectrum to higher ones . this trend 
 is visible by comparing the more dramatic decrease in absorption at 
 1679 cm to the minimal decrease in absorption 
 at 1674 and 1686 cm . therefore , changing temperature 
 is a viable method for disturbing the ldh equilibrium and can be used 
 to study the dynamics of this redistribution . the relaxation times for 
 establishing new equilibria among the ir detected substates and the 
 product states are determined by laser - induced temperature jump relaxation 
 spectroscopy employing ir probes at infrared frequencies representative 
 of each of the substates noted above . we used 1710 cm to study the free pyruvate population as well as 1704 , 1685 , 1679 , 
 and 1670 cm to study the 1703 , 1686 , 1679 , and 
 1674 cm protein - bound pyruvate bands , respectively , 
 under an assumption of one substate for each probe frequency . although 
 it is possible , and probably likely , that there are more than these 
 five pyruvate substates present and contributing overlapping signals , 
 this is the minimum number of states that can fit our equilibrium 
 data . at the probe frequencies used to study the bound pyruvate substates , 
 we can safely assume that the dominant contributor to each spectroscopic 
 signal is the assigned substate from equilibrium . using the fitting 
 parameters presented in ref ( 25 ) , we can estimate the relative contribution of each of the 
 substates to a given probe frequency . this analysis suggests that 
 the probe frequencies are dominated by the assigned substate in a 
 range of 75100% contribution . figure 3 shows the relaxation transient at 
 each probe wavelength from 10 s to 1 ms . the lower limit of 
 this range is set by the response time of the instrument , and the 
 upper limit is determined by the cooling time of the sample after 
 the temperature jump occurs ( typically several ms for this sample 
 configuration ) . the data presented in the figure represent jumps of 
 the sample to the same final temperature , 30 c , but different 
 initial temperatures . t - jumps to a final temperature of 30 c 
 optimize the change in the c2=o stretch infrared 
 absorbance from any of the lower temperatures ( figure 2 ) while avoiding cavitation artifacts observed at higher temperature . the 1710 and 1704 cm ir transients were obtained 
 with a jump from an initial temperature of 15 c . the initial 
 temperature determines the populations of the various states , whereas 
 the final temperature has a direct effect on the relaxation kinetics , 
 depending on the activation energies . the difference in the initial 
 temperatures affects the amplitude of the transients , scaling to a 
 good approximation as the size of the temperature jump . therefore , 
 the transient relaxation lifetimes for jumps to the same final temperature 
 are comparable directly , but comparison of the magnitude requires 
 adjustment to the size of the t - jump . beyond 1 ms , the solution begins 
 to cool and it is not possible to separate further changes in the 
 ir signal due to the enzyme dynamics from the cooling induced changes . the relaxation transients are all well fit to a single function , as 
 shown in figure 3 , except for the 1704 cm data . a double exponential function is required to 
 achieve a reasonable fit of the 1704 cm transient . isotope - labeled 
 ir difference temperature - jump relaxation transients 
 of [ u - n , -c]ldhnadh[2-c]pyruvate minus [ u - n , -c]ldhnadh[2-c]pyruvate at various probe frequencies . each probe frequency 
 is plotted as a different color as specified in the legend , and the 
 exponential fits are plotted as black lines . the 
 1685 , 1679 , and 1670 cm transients each 
 show a negative amplitude signal with a sub - millisecond relaxation 
 lifetime that depends on the probe frequency ; the fit lifetime decreases 
 as the probe frequency decreases . the negative amplitudes indicate 
 a net flux out of the michaelis states at the final temperature of 
 the t - jump . the observed relaxation rate at each probe frequency depends 
 on both the flux into ( the loop closure step ) and out of ( the hydride 
 transfer step ) the michaelis states . the kinetics model we developed 
 to describe the overall reaction ( described below ) indicates that 
 the relaxation is dominated by the chemistry step , leading to an overall 
 decrease in population of the michaelis states . consequently , the 
 rate of the hydride transfer is inversely correlated with the frequency 
 of the c2 carbonyl stretch ( the rate increases as the frequency decreases ) . 
 because the c2 carbonyl stretch frequency is directly related to the 
 bond strength , or the polarization of the bond , it correlates with 
 the reactivity toward hydride transfer . such a correlation is consistent 
 with previous studies relating the frequency of the c2 carbonyl vibration 
 to the rate of enzymatic turnover . previous studies generated a series of mutations 
 of ldh from b. stearothermophilus to alter the hydrogen 
 bonding network at the active site . isotope edited ftir spectroscopy 
 was used to determine the effect of these mutations on the frequency 
 of the c2 carbonyl stretch and thus how the altered hydrogen bonding 
 affects the polarity of the c2 carbonyl . these studies concluded that 
 an increase in the polarity of the bond is directly correlated to 
 an increase in the hydride transfer rate . the present work is 
 a more direct observation of the relationship 
 between carbonyl bond polarity and the rate of hydride transfer , because it compares different conformations of the same enzyme . the transients observed for the substates probed by 1685 , 1679 , 
 and 1670 cm depend on the rate of chemical transition 
 from pyruvate to lactate . this conclusion is also consistent with 
 the observation that in the equilibrium measurements this cluster 
 of infrared bands has the lowest stretch frequency and highest polarity , 
 and therefore it represents substates closest to forming lactate . importantly , the amplitudes of these transients are all negative , 
 indicating a decrease in population of the substates , due at least 
 in part to shifting the equilibrium toward lactate . furthermore , the 
 substate transients are independent in time , and there is no evidence 
 of correlated changes expected for direct interconversion of one substate 
 to another . specifically , if substate a is directly converted to substate 
 b , then we should observe a decrease in the infrared absorbance of 
 a and a corresponding increase in the infrared absorbance of b ; these 
 signals would be correlated in time with amplitudes of comparable 
 but opposite sign . we have previously observed direct interconversion 
 in studies of phldh with the michaelis complex substrate analogue , 
 oxamate . such behavior is not observed 
 in the present case . therefore , we assign this cluster of bands to 
 a set of activated conformations within a parallel reaction pathway . 
 in this context , activated indicates the complexes are ready to perform 
 chemistry , analogous to the michaelis complex in a simplified reaction 
 scheme . we have also previously reported evidence of a parallel reaction 
 pathway in the phldhnadhoxamate system . the observation that the substates follow parallel 
 pathways and have different reactivities is important because it is 
 in direct contrast to conventional enzyme models in which the chemistry 
 occurs by crossing a single dominant activation barrier . in 
 contrast , the 1704 cm transient shows a 
 positive absorbance change and the 1710 cm absorbance 
 of free pyruvate is changed very little . the 1704 cm transient is fit to a faster phase with an approximately 35 s 
 time constant that contributes 14% of the total signal intensity and 
 a slower , 500 s , phase that contributes the rest . this transient 
 forms an important counterpart to the 1685 , 1679 , and 1670 cm transients . since the 1704 cm transient has an intensity of the opposite sign and also effectively 
 spans the time scale of the lower frequency bleaches , we conclude 
 that a fraction of the population of the three michaelis complex substates 
 is transforming directly into the 1704 cm substate . the 1704 cm transient absorbance only accounts 
 for about half of the sum of the bleach features , however , meaning 
 the rest of the population of the michaelis states is converting to 
 product . we assign the 1704 cm band as an encounter 
 complex formed between ldhnadh and pyruvate at an early stage 
 of binding along the reaction pathway , characterized by weak hydrogen 
 bonding between the protein and c2=o moiety of pyruvate . evidence 
 for such a state has been observed before in other studies with phldh . the 1710 cm transient signal of free pyruvate shows a small increase on a fast 
 time scale that is not well correlated with the other signals . the 
 small magnitude of this transient and its uncorrelated time dependence 
 imply that only a small amount of free pyruvate is formed in response 
 to the t - jump , most likely from the encounter complex directly and 
 not from the michaelis states . to summarize , the transient ir 
 data indicate three features of 
 the enzyme reaction mechanism : first , the existence of several michaelis 
 complex conformations well advanced along the reaction pathway that 
 do not directly interconvert and are characterized by varied reactivity 
 for the chemical conversion of pyruvate to lactate ; second , the existence 
 of an encounter complex that interconverts to the activated conformations ; 
 third , the lack of a direct pathway between free pyruvate and the 
 michaelis states , meaning the encounter complex is an obligatory intermediate . the simplest model that incorporates all of the above conclusions 
 from the temperature - jump data is presented in scheme 1 below . additional support for this scheme comes from 
 a significant body 
 of previous work . the salient points are initial binding via the formation 
 of a weakly interacting encounter complex , protein conformational changes associated 
 with forming the michaelis complex , multiple 
 well populated conformations within the michaelis complex which do 
 not directly interconvert , and one of these populations being incompetent 
 toward conversion to lactate . a key finding from previous work is that a slow conformational motion 
 within the enzyme is likely rate limiting , not the chemistry step 
 itself . the protein motion that limits enzyme turnover involves the 
 closure of the surface loop ( residues 98110 ) to bring the 
 key residue , arg109 , into the active site ( see figure 1 ) , accompanied by changes far from the active site . this conformational change is represented in 
 scheme 1 as the transition between the encounter 
 complex ( 1704 cm ) and the reactive michaelis states . steady state kinetics measurements of the ldh enzyme yielded a kcat of 245 s with a kie 
 of 1.4 comparing enzyme loaded with nadd versus nadh . this value for the h / d primary kie is lower than expected ; 
 a characteristic value of six or more would be observed if the chemical 
 step were rate limiting . we conclude that the various protein atomic 
 rearrangements occurring within the phldhnadhpyruvate 
 complex are on a similar time scale as the chemical step ( steps 2 
 and 3 , respectively , in scheme 1 ) , such that 
 they are strongly coupled kinetically . to test the validity of scheme 1 , we developed 
 a computational routine to fit the 
 reaction scheme to previous results ( fluorescence t - jumps ) as well 
 as the new results from the ir temperature - jump data . the details 
 of this routine are discussed in the materials and 
 methods section and in the supporting information . in essence , the routine searches for rate constants to define a 
 given reaction scheme that will match input relaxation data . this 
 method incorporates all coupled reaction steps and does not require 
 making simplifying assumptions about dominant pathways . the fit data 
 in table 1 show that the transients are changing 
 on similar time scales ; therefore , making assumptions about dominant 
 pathways is unwarranted . we first attempted to fit the relaxation 
 data with the mechanism presented in scheme 1 . we used the rate constants and activation energies adapted from 
 previous optical absorption and emission t - jump studies of phldh as 
 initial guesses . however , the calculations 
 did not fit well to all of the experimental transients with the calculations 
 consistently reporting scores of 50100 ( lower is better , see 
 the materials and methods ) for the trajectories . either all of the transients except the 1704 cm transient were fit well or the 1704 cm was fit 
 well and the rest were not . figure 4a shows 
 a representative fit using the kinetics model defined by scheme 1 . step - wise adjustments to the reaction mechanism 
 were made to test how well new models fit to the experimental data . we include a representative sample of some of these other schemes 
 in the supporting information . we conclude 
 that the mechanism presented in scheme 1 is 
 not sufficient to describe the relaxation data . comparison of the simulated 
 relaxation kinetics ( dashed lines ) 
 with the experimental data ( solid lines ) . the most significant change is the better fit for the 1704 
 cm transient when scheme 2 is used . various other possible kinetic 
 schemes were tried ; these mostly 
 involved tweaking the treatment of the 1704 cm substate ( see the supporting information ) , which produced dramatic improvement of the model . we focused on 
 this substate because the results , like those of figure 4a , indicate that 1704 cm was somehow different 
 than the other substates . the best model was the inclusion of a second 
 encounter complex with the constraint that it could be populated only 
 from free pyruvate ( and hence is not along the reaction pathway to 
 lactate formation ) . scheme 2 summarizes this 
 new kinetic mechanism . in this scheme , the encounter complex state the lack of an ir signal is probably due to the heterogeneous nature 
 of this state . most likely what we are labeling as one state is in 
 reality a multitude of similar weakly bound pyruvate states along 
 a productive pathway . this heterogeneity would lead to a very broad 
 infrared band that would be hard to detect except at high concentrations . our simulations indicate that this substate has a concentration of 
 2.9 m at equilibrium . in contrast , the 1704 cm substate has a distinct , tightly bound pyruvate conformation leading 
 to a narrower ir band that allows detection of this state even at 
 low ( 3.8 m ) concentration . there is previous computational 
 evidence for an array of bound pyruvate structures in lactate dehydrogenase 
 that support this concept . the addition 
 of an additional substate resulted in two more microscopic rate constants . the result of 
 the change was to increase the overall population of this state at 
 elevated temperature in the simulation and therefore increase the 
 absorbance at 1704 cm . the model summarized 
 in scheme 2 fits the 
 experimental data well in a number of ways . it is qualitatively obvious 
 by looking at figure 4b that the new model 
 better matches each of the experimental transients than the fits shown 
 in figure 4a . quantitatively , the routine - specific 
 score values of 35 were drastically better for the new model 
 as compared to the original model s scores of 50100 . finally , we can see by comparison in table 1 that the observed relaxation lifetimes calculated by fitting the 
 theoretical transients are similar to the observed relaxation lifetimes 
 from the experimental data . the inclusion of a dead - end or noncompetent 
 state along the reaction pathway is not a new concept . we have previously 
 seen evidence for a dead - end complex when studying the phldh system 
 with the substrate mimic oxamate using infrared as the probing method . however , the oxamate work suggested the observed 
 dead - end complex was a well - populated michaelis conformation instead 
 of an encounter complex . scheme 2 is not intended 
 to assert that there are no additional michaelis conformations , or 
 that all activated conformations are productive . instead , scheme 2 is the simplest model that fits the experimental 
 data , and it supports multiple enzyme conformations at both the encounter 
 and michaelis complex stages of the reaction pathway . there is no 
 evidence for dead - end complexes when the pyruvate system is studied 
 using only nadh fluorescence as a probe . in work on a nitrated mutant enzyme , clarke and co - workers did see 
 evidence of multiple enzyme - bound pyruvate states where one such state 
 was significantly slower reacting at cryo - temperatures using stopped 
 flow . it is possible that our second encounter 
 complex may in fact be the second pathway they suggest but that it 
 is interconverting or reacting too slowly to observe in our experiments 
 and is essentially nonproductive . there are differences between 
 the experimental and simulated transients , 
 even for the best fit to scheme 2 , including 
 the best fit of the 1704 cm transient to a single 
 exponential and a longer lifetime for the 1670 cm transient in the simulation . the simulated lifetime for the 1704 
 cm transient is in between the two lifetimes of 
 the double exponential fit of the experimental data . this difference 
 is likely due to the noise and small subtraction artifacts present 
 in the experimental data that make it difficult to fit the data . the 
 simulation also predicts a longer lifetime for the 1670 cm transient than what is observed experimentally . the transient ir 
 signal for this state is very small due to its low population , making 
 it difficult to fit . it is also possible that the rate constants for 
 this state are not fully optimized in the simulation , since it only 
 contributes a small fraction of the total reaction flux . it is important 
 to point out that , despite these small discrepancies , the model still 
 predicts a decreasing lifetime with decreasing probe frequency . the defining feature of the kinetic model in scheme 2 is parallel pathways with michaelis states of varied reactivity . furthermore , the model indicates that the reactivity scales with the 
 frequency of the pyruvate c2 carbonyl stretching frequency : the lower 
 the frequency , the higher the reactivity ( shorter lifetime for the 
 chemistry step ) . this relationship can be understood in terms of the 
 relationship of the vibrational frequency to the force constant and 
 hence the bond distance or the degree of polarization of the bond . 
 in the diatomic approximation , a shift of the carbonyl mode from 1710 
 to 1679 cm represents a lengthening of the c = o 
 bond by 0.01  , making it more susceptible 
 to nucleophilic attack by the hydride . it is interesting to note that 
 the enzyme does not primarily bind pyruvate in the most reactive substate . 
 at equilibrium , the 1679 cm substate is clearly 
 the most populated one , as shown in figure 2 . since these substates do not interconvert directly , the net flux 
 through each depends on the branching from the initial encounter complex . apparently the enzyme is not optimized to primarily use the fastest 
 pathway , and the overall turnover rate is a population weighted average 
 of the multiple parallel pathways . the model outlined in scheme 2 predicts an ensemble averaged turnover rate of kcat = 179 s ( see the supporting information ) , which is similar to 
 the average turnover rate determined from nadh absorbance measurements , kcat = 245 s. thus , the ir measurements provide a high - resolution 
 view of all of the relevant substates in the enzyme reaction pathway 
 in contrast to simply observing the ensemble turnover rate . in this work , we examined the reaction pathway of pig heart ldh 
 using infrared absorbance . through analysis of equilibrium spectra , 
 relaxation transients , and subsequent kinetic modeling , we developed 
 a novel scheme for ldh catalysis that involves several branching pathways 
 and supports the presence of a dead - end complex . our results not only 
 provide direct evidence for the population of various enzyme conformations , 
 but they also indicate that the enzyme samples multiple conformations 
 while performing catalysis . this observation provides further support 
 for a dynamic view of enzyme catalysis where the role of the enzyme 
 is not just to bring reactants together but also to guide the conformational 
 search for chemically competent interactions . the inclusion 
 of substates that are off an optimal kinetic pathway 
 is particularly interesting when considering the induced fit framework 
 for understanding enzyme reactions . in this framework , the binding 
 of substrate induces conformational changes in the enzyme that are 
 necessary for catalytic action . the presence 
 of a noncompetent encounter complex complicates this framework because 
 it suggests the induced conformational change can be wrong . because 
 this noncompetent encounter complex does not convert to the competent 
 one directly this result also implies that the enzyme is not perfectly preorganized 
 for any interactions with substrate but is instead in a dynamic search 
 for the correct interaction with substrate that will lead to catalysis . the presence of similar heterogeneity in the activated conformations 
 indicates this search is not complete once substrate binds to the 
 enzyme . furthermore , 
 our results indicate that the various michaelis states are catalytically 
 competent at different rates . this finding implies that the enzyme s 
 conformational search is not necessarily for one optimal pathway or 
 conformation but simply for one that will work . the enzyme , therefore , 
 has not eliminated the search for the correct reactant interaction , 
 as compared to solution - phase chemistry , but instead provides a platform 
 for greatly reducing the search . the nonoptimized nature of many enzymes 
 has already been noted by other researchers , so it is interesting 
 to consider whether the imperfection in the search process is part 
 of the evolutionary fine - tuning of an enzyme to keep turnover rates 
 from becoming so fast as to throw off biological equilibrium . for this reason , we expect populations of catalytically 
 relevant heterogeneous structures to be an important conserved feature 
 of many enzymes .
protein 
 conformational heterogeneity and dynamics are known to 
 play an important role in enzyme catalysis , but their influence has 
 been difficult to observe directly . 
 we have studied the effects of 
 heterogeneity in the catalytic reaction of pig heart lactate dehydrogenase 
 using isotope edited infrared spectroscopy , laser - induced temperature 
 jump relaxation , and kinetic modeling . 
 the isotope edited infrared 
 spectrum reveals the presence of multiple reactive conformations of 
 pyruvate bound to the enzyme , with three major reactive populations 
 having substrate c2 carbonyl stretches at 1686 , 1679 , and 1674 cm1 , respectively . 
 the temperature jump relaxation measurements 
 and kinetic modeling indicate that these substates form a heterogeneous 
 branched reaction pathway , and each substate catalyzes the conversion 
 of pyruvate to lactate with a different rate . 
 furthermore , the rate 
 of hydride transfer is inversely correlated with the frequency of 
 the c2 carbonyl stretch ( the rate increases as the frequency decreases ) , 
 consistent with the relationship between the frequency of this mode 
 and the polarization of the bond , which determines its reactivity 
 toward hydride transfer . 
 the enzyme does not appear to be optimized 
 to use the fastest pathway preferentially but rather accesses multiple 
 pathways in a search process that often selects slower ones . 
 these 
 results provide further support for a dynamic view of enzyme catalysis 
 where the role of the enzyme is not just to bring reactants together 
 but also to guide the conformational search for chemically competent 
 interactions .