Conformational selection or induced fit: a flux description of reaction mechanism.

The mechanism of ligand binding coupled to conformational changes in macromolecules has recently attracted considerable interest. The 2 limiting cases are the "induced fit" mechanism (binding first) or "conformational selection" (conformational change first). Described here are the criteria by which the sequence of events can be determined quantitatively. The relative importance of the 2 pathways is determined not by comparing rate constants (a common misconception) but instead by comparing the flux through each pathway. The simple rules for calculating flux in multistep mechanisms are described and then applied to 2 examples from the literature, neither of which has previously been analyzed using the concept of flux. The first example is the mechanism of conformational change in the binding of NADPH to dihydrofolate reductase. The second example is the mechanism of flavodoxin folding coupled to binding of its cofactor, flavin mononucleotide. In both cases, the mechanism switches from being dominated by the conformational selection pathway at low ligand concentration to induced fit at high ligand concentration. Over a wide range of conditions, a significant fraction of the flux occurs through both pathways. Such a mixed mechanism likely will be discovered for many cases of coupled conformational change and ligand binding when kinetic data are analyzed by using a flux-based approach.

Flexibility, diversity, and cooperativity: pillars of enzyme catalysis.

This brief review discusses our current understanding of the molecular basis of enzyme catalysis. A historical development is presented, beginning with steady state kinetics and progressing through modern fast reaction methods, nuclear magnetic resonance, and single-molecule fluorescence techniques. Experimental results are summarized for ribonuclease, aspartate aminotransferase, and especially dihydrofolate reductase (DHFR). Multiple intermediates, multiple conformations, and cooperative conformational changes are shown to be an essential part of virtually all enzyme mechanisms. In the case of DHFR, theoretical investigations have provided detailed information about the movement of atoms within the enzyme-substrate complex as the reaction proceeds along the collective reaction coordinate for hydride transfer. A general mechanism is presented for enzyme catalysis that includes multiple intermediates and a complex, multidimensional standard free energy surface. Protein flexibility, diverse protein conformations, and cooperative conformational changes are important features of this model.

Analysis of the eukaryotic topoisomerase II DNA gate: a single-molecule FRET and structural perspective.

Type II DNA topoisomerases (topos) are essential and ubiquitous enzymes that perform important intracellular roles in chromosome condensation and segregation, and in regulating DNA supercoiling. Eukaryotic topo II, a type II topoisomerase, is a homodimeric enzyme that solves topological entanglement problems by using the energy from ATP hydrolysis to pass one segment of DNA through another by way of a reversible, enzyme-bridged double-stranded break. This DNA break is linked to the protein by a phosphodiester bond between the active site tyrosine of each subunit and backbone phosphate of DNA. The opening and closing of the DNA gate, a critical step for strand passage during the catalytic cycle, is coupled to this enzymatic cleavage/religation of the backbone. This reversible DNA cleavage reaction is the target of a number of anticancer drugs, which can elicit DNA damage by affecting the cleavage/religation equilibrium. Because of its clinical importance, many studies have sought to determine the manner in which topo II interacts with DNA. Here we highlight recent single-molecule fluorescence resonance energy transfer and crystallographic studies that have provided new insight into the dynamics and structure of the topo II DNA gate.

Recommendations for terminology and databases for biochemical thermodynamics.

Chemical equations are normally written in terms of specific ionic and elemental species and balance atoms of elements and electric charge. However, in a biochemical context it is usually better to write them with ionic reactants expressed as totals of species in equilibrium with each other. This implies that atoms of elements assumed to be at fixed concentrations, such as hydrogen at a specified pH, should not be balanced in a biochemical equation used for thermodynamic analysis. However, both kinds of equations are needed in biochemistry. The apparent equilibrium constant K' for a biochemical reaction is written in terms of such sums of species and can be used to calculate standard transformed Gibbs energies of reaction Δ(r)G'°. This property for a biochemical reaction can be calculated from the standard transformed Gibbs energies of formation Δ(f)G(i)'° of reactants, which can be calculated from the standard Gibbs energies of formation of species Δ(f)G(j)° and measured apparent equilibrium constants of enzyme-catalyzed reactions. Tables of Δ(r)G'° of reactions and Δ(f)G(i)'° of reactants as functions of pH and temperature are available on the web, as are functions for calculating these properties. Biochemical thermodynamics is also important in enzyme kinetics because apparent equilibrium constant K' can be calculated from experimentally determined kinetic parameters when initial velocities have been determined for both forward and reverse reactions. Specific recommendations are made for reporting experimental results in the literature.

Free-energy landscape of enzyme catalysis.

The concept is developed that enzyme mechanisms should be viewed as "catalytic networks" with multiple conformations that occur serially and in parallel in the mechanism. These coupled ensembles of conformations require a multi-dimensional standard free-energy surface that is very "rugged", containing multiple minima and transition states. Experimental and theoretical evidence is presented to support this concept.

Single-molecule measurements of the opening and closing of the DNA gate by eukaryotic topoisomerase II.

Type II DNA topoisomerases are essential and ubiquitous enzymes that perform important functions in chromosome condensation and segregation and in regulating intracellular DNA supercoiling. Topoisomerases carry out these DNA transactions by passing one segment of DNA through the other by using a reversible, enzyme-bridged double strand break. The transient enzyme/DNA adduct is mediated by a phosphodiester bond between the active-site tyrosine and a backbone phosphate of DNA. The opening and closing of the DNA gate, a critical step for strand passage during the catalytic cycle, is coupled to this cleavage/religation. We designed a unique oligonucleotide substrate with a pair of fluorophores straddling the topoisomerase II cleavage site, allowing the use of FRET to monitor the opening of the DNA gate. The DNA substrate undergoes an enzyme-mediated transition between a closed and open state in the presence of ATP, similar to the overall topoisomerase II catalyzed reaction. Single-molecule fluorescence microscopy measurements demonstrate that the transition has comparable rate constants for both the opening and closing reaction during steady-state ATP hydrolysis, with an apparent equilibrium constant near unity. In the presence of AMPPNP, a reduction in FRET occurs, suggesting an opening or partial opening of the DNA gate. However, the single-molecule experiments indicate that the open and closed states do not interconvert at a measurable rate.

Folding mechanism of a multiple independently-folding domain protein: double B domain of protein A.

The antibody binding properties of staphylococcal protein A (SpA) can be attributed to the presence of five highly homologous domains (E, D, A, B, and C). Although the folding of the B domain of protein A (BdpA) is well-characterized, the folding behavior of this domain in the context of full-length SpA in the cell remains unexplored. The sequence of the B domain is 89 and 91% identical to those of domains A and C, respectively. We have fused B domain sequences (BBdpA) as a close approximation of the A-B or B-C portion of SpA. Circular dichroism and fluorescence-detected denaturation curves of BBdpA are experimentally indistinguishable from those of BdpA. The rate constants for folding and unfolding from NMR line shape analysis for the single- and double-domain proteins are the same within experimental uncertainties (+/-20%). These results support the designation of SpA as a multiple independently-folding domain (MIFD) protein. We develop a mathematical model that describes the folding thermodynamics and kinetics of MIFD proteins. The model depicts MIFD protein folding and unfolding as a parallel network and explicitly calculates the flux through all parallel pathways. These fluxes are combined to give a complete description of the global thermodynamics and kinetics of the folding and unfolding of MIFD proteins. The global rates for complete folding and unfolding of a MIFD protein and those of the individual domains depend on the stability of the protein. We show that the global unfolding rate of a MIFD protein may be many orders of magnitude slower than that of the constituent domains.

Single-molecule investigation of the T4 bacteriophage DNA polymerase holoenzyme: multiple pathways of holoenzyme formation.

In T4 bacteriophage, the DNA polymerase holoenzyme is responsible for accurate and processive DNA synthesis. The holoenzyme consists of DNA polymerase gp43 and clamp protein gp45. To form a productive holoenzyme complex, clamp loader protein gp44/62 is required for the loading of gp45, along with MgATP, and also for the subsequent binding of polymerase to the loaded clamp. Recently published evidence suggests that holoenzyme assembly in the T4 replisome may take place via more than one pathway [Zhuang, Z., Berdis, A. J., and Benkovic, S. J. (2006) Biochemistry 45, 7976-7989]. To demonstrate unequivocally whether there are multiple pathways leading to the formation of a productive holoenzyme, single-molecule fluorescence microscopy has been used to study the potential clamp loading and holoenzyme assembly pathways on a single-molecule DNA substrate. The results obtained reveal four pathways that foster the formation of a functional holoenzyme on DNA: (1) clamp loader-clamp complex binding to DNA followed by polymerase, (2) clamp loader binding to DNA followed by clamp and then polymerase, (3) clamp binding to DNA followed by clamp loader and then polymerase, and (4) polymerase binding to DNA followed by the clamp loader-clamp complex. In all cases, MgATP is required. The possible physiological significance of the various assembly pathways is discussed in the context of replication initiation and lagging strand synthesis during various stages of T4 phage replication.

Conformation coupled enzyme catalysis: single-molecule and transient kinetics investigation of dihydrofolate reductase.

Ensemble kinetics and single-molecule fluorescence microscopy were used to study conformational transitions associated with enzyme catalysis by dihydrofolate reductase (DHFR). The active site loop of DHFR was labeled with a fluorescence quencher, QSY35, at amino acid position 17, and the fluorescent probe, Alexa555, at amino acid 37, by introducing cysteines at these sites with site-specific mutagenesis. The distance between the probes was such that approximately 50% fluorescence resonance energy transfer (FRET) occurred. The double-labeled enzyme retained essentially full catalytic activity, and stopped-flow studies of both the forward and reverse reactions revealed that the distance between probes increased prior to hydride transfer. A fluctuation in fluorescence intensity of single molecules of DHFR was observed in an equilibrium mixture of substrates but not in their absence. Ensemble rate constants were derived from the distributions of lifetimes observed and attributed to a reversible conformational change. Studies were carried out with both NADPH and NADPD as substrates, with no measurable isotope effect. Similar studies with a G121V mutant DHFR resulted in smaller rate constants. This mutant DHFR has reduced catalytic activity, so that the collective data for the conformational change suggest that the conformational change being observed is associated with catalysis and probably represents a conformational change prior to hydride transfer. If the change in fluorescence is attributed to a change in FRET, the distance change associated with the conformational change is approximately 1-2 A. These results are correlated with other measurements related to conformation coupled catalysis.

Interaction between the T4 helicase loading protein (gp59) and the DNA polymerase (gp43): unlocking of the gp59-gp43-DNA complex to initiate assembly of a fully functional replisome.

Single-molecule fluorescence resonance energy transfer and functional assays have been used to study the initiation and regulation of the bacteriophage T4 DNA replication system. Previous work has demonstrated that a complex of the helicase loading protein (gp59) and the DNA polymerase (gp43) on forked DNA totally inhibits the polymerase and exonuclease activities of gp43 by a molecular locking mechanism (Xi, J., Zhuang, Z., Zhang, Z., Selzer, T., Spiering, M. M., Hammes, G. G., and Benkovic, S. J. (2005) Biochemistry 44, 2305-2318). We now show that this complex is "unlocked" by the addition of the helicase (gp41) with restoration of the DNA polymerase activity. Gp59 retains its ability to load the helicase while forming a gp59-gp43 complex at a DNA fork in the presence of the single-stranded DNA binding protein (gp32). Upon the addition of gp41 and MgATP, gp59 dissociates from the complex, and the DNA-bound gp41 is capable of recruiting the primase (gp61) to form a functional primosome and, subsequently, a fully active replisome. Functional assays of leading- and lagging-strand synthesis on an active replication fork show that the absence of gp59 has no effect on the coupling of leading- and lagging-strand synthesis or on the size of the Okazaki DNA fragments. We conclude that gp59 acts in a manner similar to the clamp loader to ensure proper assembly of the replisome and does not remain as a replisome component during active replication.

Interaction between the T4 helicase-loading protein (gp59) and the DNA polymerase (gp43): a locking mechanism to delay replication during replisome assembly.

The T4 helicase-loading protein (gp59) has been proposed to coordinate leading- and lagging-strand DNA synthesis by blocking leading-strand synthesis during the primosome assembly. In this work, we unambiguously demonstrate through a series of biochemical and biophysical experiments, including single-molecule fluorescence microscopy, that the inhibition of leading-strand holoenzyme progression by gp59 is the result of a complex formed between gp59 and leading-strand polymerase (gp43) on DNA that is instrumental in preventing premature replication during the assembly of the T4 replisome. We find that both the polymerization and 3' --> 5' exonuclease activities of gp43 are totally inhibited within this complex. Chemical cross-linking of the complex followed by tryptic digestion and peptide identification through matrix-assisted laser desorption/ionization-time-of-flight (MALDI-TOF) mass spectrometry identified Cys169 of gp43 and Cys215 of gp59 as residues in a region of a protein-protein contact. With the available crystal structures for both gp43 and gp59, a model of the complex was constructed based on shape complementarity, revealing that parts of the C-terminal domain from gp59 insert into the interface created by the thumb and exonuclease domains of gp43. This insertion effectively locks the polymerase into a conformation where switching between the pol and editing modes is prevented. Thus, continued assembly of the replisome through addition of the primosome components and elements of the lagging-strand holoenzyme can occur without leading-strand DNA replication.

Assembly of the bacteriophage T4 primosome: single-molecule and ensemble studies.

Within replisomes for DNA replication, the primosome is responsible for unwinding double-stranded DNA and synthesizing RNA primers. Assembly of the bacteriophage T4 primosome on individual molecules of ssDNA or forked DNA (fDNA) has been studied by using FRET microscopy. On either DNA substrate, an ordered process of assembly begins with tight 1:1 binding of ssDNA-binding protein (gp32) and helicase-loading protein (gp59) to the DNA. Magnesium adenosine 5'-O-(3-thiotriphosphate) (MgATPgammaS) mediates the weak binding of helicase (gp41) to DNA coated with gp32 and gp59, whereas MgATP induces gp32 and gp59 to dissociate, leaving gp41 bound to the DNA. Finally, primase (gp61) binds to the gp41.DNA complex. Ensemble studies were used to determine protein stoichiometries and binding constants. These single-molecule studies provide an unambiguous description of the pathway for assembly of the primosome on the lagging strand of DNA at a replication fork.

Multiple conformational changes in enzyme catalysis.

Understanding the molecular mechanisms of enzyme catalysis and allosteric regulation has been a primary goal of biochemistry for many years. The dynamics of these processes, approached through a variety of kinetic methods, are discussed. The results obtained for many different enzymes suggest that multiple intermediates and conformations are general characteristics of the catalytic process and allosteric regulation. Ribonuclease, dihydrofolate reductase, chymotrypsin, aspartate aminotransferase, and aspartate transcarbamoylase are considered as specific examples. Typical and maximum rates of conformational changes and catalysis are also discussed, based on results obtained from model systems. The nature and rates of interconversion of the intermediates, along with structural information, can be used as the bases for understanding the incredible catalytic efficiency of enzymes. Potential roles of conformational changes in the catalytic process are discussed in terms of static and environmental effects, and in terms of dynamic coupling within the enzyme-substrate complex.

Single-molecule and transient kinetics investigation of the interaction of dihydrofolate reductase with NADPH and dihydrofolate.

The interaction of dihydrofolate (H(2)F) and NADPH with a fluorescent derivative of H(2)F reductase (DHFR) was studied by using transient and single-molecule techniques. The fluorescent moiety Alexa 488 was attached to the structural loop that closes over the substrates after they are bound. Fluorescence quenching was found to accompany the binding of both substrates and the hydride transfer reaction. For the binding of H(2)F to DHFR, the simplest mechanism consistent with the data postulates that the enzyme exists as slowly interconverting conformers, with the substrate binding preferentially to one of the conformers. At pH 7.0, the binding reaction has a bimolecular rate constant of 1.8 x 10(7) M(-1).s(-1), and the formation of the initial complex is followed by a conformational change. The binding of NADPH to DHFR is more complex and suggests multiple conformers of the enzyme exist. NADPH binds to a different conformer than H(2)F with a bimolecular rate constant of 2.6-5.7 x 10(6) M(-1).s(-1), with the former value obtained from single-molecule kinetics and the latter from stopped-flow kinetics. Single-molecule studies of DHFR in equilibrium with substrates and products revealed a reaction with ensemble average rate constants of 170 and 470 s(-1) at pH 8.5. The former rate constant has an isotope effect of >2 when NADPD is substituted for NADPH and probably is associated with hydride transfer. The results from stopped-flow and single-molecule methods are complementary and demonstrate that multiple conformations of both the enzyme and enzyme-substrate complexes exist.

Interaction of dihydrofolate reductase with methotrexate: ensemble and single-molecule kinetics.

The thermodynamics and kinetics of the interaction of dihydrofolate reductase (DHFR) with methotrexate have been studied by using fluorescence, stopped-flow, and single-molecule methods. DHFR was modified to permit the covalent addition of a fluorescent molecule, Alexa 488, and a biotin at the N terminus of the molecule. The fluorescent molecule was placed on a protein loop that closes over methotrexate when binding occurs, thus causing a quenching of the fluorescence. The biotin was used to attach the enzyme in an active form to a glass surface for single-molecule studies. The equilibrium dissociation constant for the binding of methotrexate to the enzyme is 9.5 nM. The stopped-flow studies revealed that methotrexate binds to two different conformations of the enzyme, and the association and dissociation rate constants were determined. The single-molecule investigation revealed a conformational change in the enzyme-methotrexate complex that was not observed in the stopped-flow studies. The ensemble averaged rate constants for this conformation change in both directions is about 2-4 s(-1) and is attributed to the opening and closing of the enzyme loop over the bound methotrexate. Thus the mechanism of methotrexate binding to DHFR involves multiple steps and protein conformational changes.