The Contribution of Atomic Motion to Enzyme Function
The Dynamical Nature of Proteins
It is well known that atomic motion in proteins, over broad time scales, contributes to enzymic catalysis. However, the specific types of motions in binding and transition state formation have not been well characterized for any enzyme system. Partly, this is because new approaches are needed to work out the dynamical nature of enzyme catalysis; the transition state is far from equilibrium but is the most relevant instant of enzymatic function. We are developing new experimental and theoretical approaches that are effective in understanding the dynamical nature of proteins broadly and enzymatic catalysis specifically. We combine time resolved approaches (laser induced temperature jump, ultrafast microfluidic mixing, nanosecond and picosecond laser spectroscopies) with transition state analysis and innovative computational analysis (molecular dynamics coupled with transition path sampling) and apply these unique and powerful battery of methods to examine the dynamics related to enzymatic catalysis on all relevant time scales (from femtoseconds to minutes). Sparsely populated intermediates, complicated kinetic pathways, and states important for the catalytic pathway far from equilibrium are accessible to our combined spectroscopic, kinetic isotope effect, and computational approaches.
We have evidence that atomic motion at all time scales, from femtoseconds to milliseconds contributes to mechanism in enzymatic catalysis; we discuss this briefly below (1-6, 10). This notion is really not a surprise. It has long been recognized that a protein does not occupy a unique folded single three dimensional array of atoms. Rather, the protein's structure is described by occupying a hierarchy or ensemble of interconverting conformations on all time scales, from picosecond to minutes, and spatial extent from small atom displacements to large scale domain motions. This physical picture flows from the fact that a protein is a finite assembly of atoms whose structural integrity is dictated by a large number of weak forces acting together. This exact nature of its dynamical nature is directed by its so-called 'energy landscape'. This organizing concept is useful in understanding the dynamical contribution to function since it permits a framework in designing specific studies and thier analysis (see ref. 8).
A highly simplified picture of an idealized energy landscape and the relationship to enzymic catalysis is given by the scheme below. The diagram emphasizes that substrate binding proceeds through an ensemble of interconverting protein conformations, some competent to bind substrate and some not. The Michaelis complex is not the single conformation as depicted in most textbooks but is also an ensemble of interconverting conformations, but a restricted ensemble. In principle, the conformational phase space available to enzymes, specifically to the Michaelis complex, is huge. Akin to the protein 'folding problem', an enzyme limits it's search through configuration space using 'functionally important' motions as the reaction proceeds from substrate to product. The conformations available to the Michaelis complex must be quite restricted so that the search can come to its completion in the ca. one ms time characterizing enzymatic catalysis. We view the search process as being basically 'stochastic'. The atoms of the system samples their allowable positions and momenta in a random search until the transition state is reached. In our work to date (on an admittedly limited number of systems and situations), we find the time scales of functionally important motions occur on all time scales: picosecond-femtosecond, nanoseconds, microseconds, milliseconds. Finally, we have found also that the vibrational motions (one the picosecond-femtosecond time scale) of organized protein strcuture, called 'promoting vibrations, help carry the system past the transition state.
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An energy landscape picture of enzymatic catalysis. Binding of substrate involves specific conformations of the enzyme ensemble of conformations which are competent to bind. The Michaelis complex is an ensemble of interconverting states, some of which are far from being productive and some closer to the transition state. Organized portions of the protein form a sub-ps compression mode, 'promoting vibrations', that carries the system over the transition state. The picture emphasizes the energy landscape with regards to the entire protein-ligand complex. The reaction coordinate of the reacting groups is a specific coordinate subspace embedded within the protein-ligand energy landscape. Shown in color (black, to blue, to green, to red), the approach to the transition state of the system is indicated. The putative pathways between conformations is highly simplified. |
Much of our work in this area is supported by a GM (National Institutes of Health General Medicine) sponsored Program Project (see Program's web site). This project is a collaborative venture involving the
laboratories of Vern Schramm (The Schramm Lab), Steve Schwartz (The Schwartz Lab), and Bob Callender at Albert Einstein, and Brian Dyer (The Dyer Lab) at Emory University. In addition, work supported by National Institute of Biomedical Imaging and Bioengineering develops and then applies new advanced methods of imaging, or 'seeing', the motion of the atoms within proteins while they are functioning. The fruits of both studies should lead to a thorough understanding of some diseases, and can lead to new drugs as well as laboratory diagnostic methods.
We sketch some of the findings below, mostly focussing on our work concerning lactate dehydrogenase (LDH).
THE DYNAMICS OF BINDING SUBSTRATE
We have studied in some detail how the substrate binds to the LDH/NADH enzyme/cofactor complex (3,4). We were able to infer a plausible structure for the binding competent species of LDH from our experimental and theoretical work. First, the binding non-competent species of LDH complexed with its NADH cofactor is as pictured in the crystallographic pictures: the substrate binding site (given in red in the figure below) is fairly buried into the protein (10 Å from the surface), and the surface loop that covers the binding pocket is 'closed'. This conformation is, perhaps quite surprisingly, in the majority, perhaps 10 times the population of the those LDH/NADH conformations competent to bind the substrate. In th binding competent conformations, our results suggest that the 'mobile loop' of LDH is partially open; the ensemble contains multiple open conformations, yielding multiple binding pathways. These 'open' conformations do not require large scale unfolding/melting of the LDH/NADH enzyme/cofactor complex. Rather, 'open' versus 'closed' structures differ via subtle protein and water rearrangements. The binding competent species can bind ligand at or very near diffusion limited speeds, suggesting that the binding pocket is substantially exposed to solvent in these species, as is predicted by our computational studies. We speculate that such a strategy for binding, effectively a transient exposure of the binding pocket to solvent, may be necessary to get a ligand efficiently to a binding pocket that is located fairly deep within the protein's interior. Such a process is a fairly old idea; some sort of transient dynamical motion(s) was postulated, from the days of the first crystallographic pictures, to be required for the binding of oxygen to myoglobin and hemoglobin since the binding pocket in these proteins is deeply buried indeed.
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The channel to the active site of LDH/NADH in a the closed (left) and open (right) form. The coloring scheme is consistent to both pictures: white - Arg109; dark blue - loop residues except Arg109 (98:105 and 107:110); red - Asn138, Arg169, His193, Thr248; light blue - rest of the protein. Arg109 is displaced 5.64 Å from its position in the active site into the surface of the protein. |
During cell volume regulation, intracellular concentration changes occur in both inorganic (e.g., salts) and organic osmolytes (e.g., urea, trimethylamine N-oxide) in order to balance the extracellular osmotic stress and maintain cell volume homeostasis. Generally, salt and urea increase the Kms of enzymes and TMAO counteracts these effects by decreasing Kms. The standard hypothesis to account for these effects is that urea and salt shift the native state ensemble of the enzyme toward conformers that are substrate binding incompetent (BI), while TMAO shifts the ensemble toward binding competent (BC) species. Our work directly confirmed this in quite detailed studies on lactate dehydrogenase (3) and triosephosphate isomerase (TIM; 7). We were also able to measure the effects of osmolytes of the individual rate constants along the ligand binding pathway of the binding competent TIMs. This is important because Kms are often complex assemblies of rate constants involving several elementary steps in catalysis. Our results indicate the osmolytes not only affect the equilibrium between BI and BC TIM conformations but ALSO affect other rate constants along the binding pathway.
THE MICHAELIS COMPLEX: "Functionally Important Motions"
The energy landscape scheme given above suggests that there are several populated conformations of the Michaelis complex, which for studies on lactate dehydrogenase is the LDH/NADH/pyruvate ternary complex, some of which may be 'closer to' the transition state than others. From the cartoon of the active structure showing bound NADH and pyruvate (below), it is easily seen that two main features dominate the catalytic prowess of LDH: (1) NADH and pyruvate are brought in a correct alignment and in close proximity and (2) the (quite strong) hydrogen bonds between the C=O group of pyruvate and key active site residues substantially lowers the barrier for the conversion of pyruvate to the alcohol lactate. LDH catalyzes the pyruvate-lactate interconversion by some 14-orders of magnitude. Proximity (along with orientation) and C=O bond polarization each contribute roughly half to rate enhancement as deduced from various physical and biochemical studies.
At right is a cartoon of NADH and pyruvate bound to LDH with important active site residues shown (using the standard numbering system). The His195/Asp168 dyad is essential for catalysis. N3 of the protonated imidizole ring of His195 approaches the carbonyl ring oxygen of pyruvate at an angle that is optimal for proton transfer which must occur in the pyruvate to lactate transformation. In addition, a strong hydrogen bond is formed between the His195 and the substrate carbonyl oxygen which polarizes the C=O bond. Another important structural attribute of the enzyme is the surface loop of the polypeptide chain (residues 98-110, the so-called 'mobile loop') which is said to 'close over' the bound substrate ligand; this change in conformation also brings the catalytically important Arg109 into the active site, forming another hydrogen bond with the substrate C=O group. |
The 'clssical' view of the reaction coordinate of LDH is quite simple; it involves the more or less concerted transfer of a hydride ion from the C4 atom of NADH to C2 of pyruvate and a proton from His195 to oxygen (9). As is discussed below, this view is much too simplified; the on-enzyme reaction coordinate also involves protein residues. Takingthat the standard view, emphasizing static structures, has it that the enzyme-substrate complex is sort of 'frozen' into the appropriate conformation to lower the transition state energy with the system awaiting to gain sufficient thermal energy to lift it from the ground state conformation to, and then over, the transition state. But suppose that the system can adopt a range of conformations so that some conformations find themselves with a NADH-pyruvate distance too large or with distances between the hydrogen bond donors and the C=O group too large for efficient hydride-proton transfer. Indeed, a preliminary computational study of LDH/NADH/pyruvate structures has indeed suggested that the complex is an ensemble of structures with the NADH-pyruvate distance of most of them too large for hydride transfer (8).
The strong hydrogen bonds between the C=O group of pyruvate and His195 and Arg109 polarize the carbonyl bond and lower its stretch frequency. In fact, there is a strong correlation between the C=O stretch frequency and catalytic activity (9), as would be expected. Hence, we have recently performed a study measuring the IR spectrum of pyruvate bound to LDH/NADH, the Michaelis complex for LDH. The data is given in the next figure. It is observed that pyruvate in solution shows a single (wide) band centered at approximately 1709 cm-1. The protein bound molecule, on the contrary, shows two bands shifted from the solution value (1679 and 1686 cm-1) and a grouping of bands near the solution value. IR spectroscopy has a characteristic time scale in the femtosecond domain. Hence, the observed bands represent various conformations of the protein complex with their relative populations indicated by relative band strengths. This is clear proof of an ensemble of states, some more catalytic competent than others (the lower the frequency the higher the catalytic competence with a ca. 30 cm-1 difference in frequency representing a six-orders of magnitude in kcat). Studies of Michaelis complex mimics show similar heterogeneity (2, 6). The interconversion times between the various conformations in those systems range from 1-1000 microseconds.
In blue, the IR spectrum of pyruvate in solution. Note the single, if broad, band near 1709 cm-1. In red, the difference spectrum formed by subtracting LDH/NADH/[12C2]pyruvate from LDH/NADH/[13C2]pyruvate. This procedure isolates the C2=O stretch in the spectrum. Note there are several bands, some quite down-shifted, at various positions that are more or less similarly populated. |
PROMOTING VIBRATIONS
Work performed by the Schwartz lab shows unambigously that the reaction coordinate of the LDH catalyzed reaction involves a specific set of protein residues, in addition to key coordinates located on the substrates (10-11). These organized motions in LDH occur on the subpicosecond time scale (corresponding frequencies of ca. 150 cm-1) and have been called a promoting vibration within the protein matrix. For LDH, they act as a compression mode, that strongly couples to and modulates the on-enzyme reaction coordinate so as to bring about an increase in reaction rate. These are thought to be true vibrational modes. The Figure belows shows the line of residues involved for bsLDH. The mode, as can be seen, is extended through the protein from the surface to the interior. The motion includes a compression towards the reacting substrates, which brings the NADH ring closer to C2 of bound pyruvate in a proper geometry for reaction. This is followed by a relaxation which tends to drive the system to completion, from substrate to product if the substrate side is the starting point.
The Figure above shows a monomer of (Bacillus stearothermophilus) bsLDH with atoms in the active site highlighted, specifically, the nicotinamide ring, substrate, active site histidine (red) and donor/acceptor axis residues (green and blue). |
Val31, Ala32, Gly33, Phe65, Asn66 (in green) compressed towards the active site bringing C4 of the nicotinamide ring and substrate carbon closer together while Arg106 (blue) relaxes away locking the substrate in product formation. These residues span the entire length of the monomer to the edge of the protein. The residue numbering system is specific for bsLDH; Arg106 corresponds to Arg109 in the conventional system. |
REFERENCES
1. Zhadin, N., M. Gulotta, and R. Callender. Probing the Role of Dynamics in Hydride Transfer Catalyzed by Lactate Dehydrogenase. Biophysical J. 95: 1974-1984, 2008.
2. Deng, H., S.H. Brewer, D.V. Vu, K. Clinch, R. Callender, and R.B. Dyer. On the Pathway of Forming Enzymatically Productive Ligand-Protein Complexes in Lactate Dehydrogenase. Biophysical J. 95: 804-813, 2008.
3. Qiu, L., M. Gulotta, and R. Callender. Lactate Dehydrogenase Undergoes a Substantial Structural Change to Bind its Substrate. Biophysical J. 93: 1677-1686, 2007.
4. Pineda, J.R.E.T., R. Callender, and S.D. Schwartz. Ligand Binding and Protein Dynamics in Lactate Dehydrogenase. Biophysical J. 93: 1474-1483, 2007.
5. McClendon, S., N. Zhadin, and R. Callender. The Approach to the Michaelis Complex in Lactate Dehydrogenase: the substrate binding pathway. Biophysical J. 89: 2024-2032, 2005.
6. McClendon, S., D. Vu, K. Clinch, R. Callender, and R.B. Dyer. Structural Transformations in the Dynamics of Michaelis Complex Formation in Lactate Dehydrogenase. Biophysical J. 89: L07-L09, 2005.
7. Gulotta, M., L. Qiu, J.
Rosgen, D.W. Bolen, and R. Callender. Effects of Cell Volume Regulating Osmolytes on Glycerol-3-phosphate Binding to Triosphosphate Isomerase. Biochemistry 46: 10055-10062, 2007.
8. Pineda, E. T., and Schwartz, S. D. (2006) Protein Dynamics and Catalysis – The Problems of Transition State Theory and the Subtlety of Dynamic Control. Phil. Trans. Royal Soc. 361, 1433-1438.
9. Deng, H., Zheng, J., Clarke, A., Holbrook, J. J., Callender, R., and Burgner, J. W. (1994) Source of Catalysis in the Lactate Dehydrogenase System: Ground State Interactions in the Enzyme-Substrate Complex. Biochemistry 33, 2297-2305.
10. Quaytman, S.L. and S.D. Schwartz. 2007. Reaction Coordinate of an Enzymic Reaction Revealed by Transition Path Sampling. Proc. Natl. Acad. Sci. (USA) 104: 12253-12258.
11. Basner, J.E. and S.D. Schwartz. 2004. Donor-Acceptor Distance and Protein Promoting Vibration Coupling to Hydride Transfer: A possible mechanism for kinetic control in isozymes of human lactate dehydrogenase. J. Phys. Chem. B 108: 444-451.