Time course of ATP (■), CTP (□), and GTP (△) hydrolysis by a single, noninteracting site of the DnaB helicase hexamer in single-turnover experiments in buffer T4. The produced NDPs (ADP, CDP, and GDP) are shown as fractions of the total concentration of the corresponding NTPs (ATP, CTP, and GTP) in the sample. The concentrations of the cofactors were 1.9 × 10⁻⁷ M. The concentration of the enzyme was 7.5 × 10⁻⁶ M (protomer). The solid lines are the nonlinear least-squares fits of the double-exponential function (eq 1) to the experimental kinetic curves (details in the text).

Sedimentation velocity absorption profiles, recorded at 485 nm, of the ssDNA 20-mer, 5′-Pl-dA(pA)₁₉, in the presence of the DnaB helicase in buffer T4, in the absence of nucleotide cofactors. The concentrations of the nucleic acid and the helicase were 3 × 10⁻⁶ M (oligomer) and 3 × 10⁻⁵ M (hexamer), respectively. The scans were collected at 30000 rpm. The short initial parts of the scans correspond to the buffer–air region above the sample meniscus. The arrows indicate the absorption of the total concentration of 5′-Fl-dA(pA)₁₉ (T), the concentration of the 20-mer bound to the DnaB helicase (C), and the concentration of the free 20-mer (F). The horizontal lines indicate the locations of the plateaus corresponding to the zero line, free, 5′-Fl-dA(pA)₁₉, concentration and the total, 5′-Fl-dA(pA)₁₉, concentration (see the text for details).

(a) Time course of ATP hydrolysis by a single, noninteracting site of the DnaB helicase hexamer in the presence of the ssDNA 20-mer, dC(pC)₁₉ (■), in single-turnover experiments, in buffer T4. The produced ADP is shown as a fraction of the total concentration of the ATP in the sample. The concentrations of the cofactor and the enzyme were 1.9 × 10⁻⁷ M and 7.5 × 10⁻⁶ M (protomer), respectively. The concentration of the nucleic acid was 6.5 × 10⁻⁵ M (oligomer). For the sake of companson, the time course of ATP hydrolysis by a single, noninteracting site of the DnaB helicase hexamer in the absence of the ssDNA 20-mer is included in the panel, at the same cofactor and enzyme concentrations (□). The solid line is the nonlinear least-squares fit of the double-exponential function (eq 1) to the experimental curve. (b) Dependence of the reciprocal of the relaxation time, 1/τ₁, for ATP hydrolysis by the single, noninteracting site of the DnaB helicase in buffer T4, in the presence of dC(pC)₁₉, on the total concentration of the enzyme (protomer). The solid line is a numerical, nonlinear least-squares fit of the experimental data to the three-step sequential mechanism, defined by Scheme 1. (c) Dependence of the reciprocal of the relaxation time, 1/τ₂, for ATP hydrolysis by the single, noninteracting site of the DnaB helicase in buffer T4, in the presence of dC(pC)₁₉, on the total concentration of the enzyme (protomer). The solid line is a numerical, nonlinear least-squares fit of the experimental data to the three-step sequential mechanism, defined by Scheme 1. The error bars in panels b and c are standard deviations determined in three normalized total and individual relaxation amplitudes, A_T (▲), A₁ (■), and A₂ (□), of ATP hydrolysis by a single, noninteracting site of the DnaB helicase in buffer T4, in the presence of dC(pC)₁₉, on the total concentration of the enzyme (protomer). The solid lines are nonlinear least-squares fits according to the three-step sequential mechanism of ATP hydrolysis in the noninteracting site of the helicase, described by Scheme 1. The rate constants, obtained from the fits of the relaxation times and the amplitudes, are included in Table 1.

Schematic structure of the DnaB hexamer–ssDNA complex based on thermodynamics, fluorescence energy transfer studies, and biochemical data (24, 25, 27, 58). Each DnaB subunit is built of a small ~12 kDa domain and a large ~33 kDa domain. The total ssDNA-binding site occludes ~20 nucleotides of the DNA. The strong DNA-binding subsite is located in the vicinity of the 12 kDa domain and occludes ~10 nucleotides at the 5′ end of the bound nucleic acid. The weak DNA-binding subsite occludes a similar number of ~10 nucleotides and is located in the 33 kDa domain of the helicase. The yellow oval indicates the location of the NTP-binding site. The arrows indicate the functional directions of the allosteric effects of the nucleic acid on the NTPase site of the enzyme. The strong DNA-binding subsite directly interacts with the NTPase site. The effect of the weak DNA-binding subsite is indirect, through its modulation of the DNA structure in the strong subsite.

Time course of CTP hydrolysis by a single, noninteracting site of the DnaB helicase hexamer in the presence of the ssDNA 20-mers dC(pC)₉(pA)₁₀ (▲), dA(pA)₉(pC)₁₀ (△), and dA(pA)₁₉ (□), in single-turnover experiments, in buffer T4. The produced CDP is shown as a fraction of the total concentration of the CTP in the sample. The concentrations of the cofactor and the enzyme were 1.9 × 10⁻⁷ M and 7.5 × 10⁻⁶ M (protomer), respectively. The concentrations of all nucleic acids were 6.5 × 10⁻⁵ M (oligomer). The solid lines are the nonlinear, least-squares fits of the double-exponential function (eq 1) to the experimental kinetic curves (details in the text).

(a) Dependence of the reciprocal of the relaxation time, 1/τ₁, for CTP hydrolysis by the single, noninteracting site of the DnaB helicase in buffer T4, in the presence of dC(pC)₉(pA)₁₀, on the total concentration of the enzyme (protomer). The solid line is a nonlinear, least-squares fit of the experimental data to the three-step sequential mechanism, defined by Scheme 1. (b) Dependence of the reciprocal of the relaxation time, 1/τ₂, for CTP hydrolysis by the single, noninter-acting site of the DnaB helicase in buffer T4, in the presence of, dC(pC)₉(pA)₁₀, on the total concentration of the enzyme (protomer). The solid line is a nonlinear, least-squares fit of the experimental data to the three-step sequential mechanism, defined by Scheme 1. The error bars in panels a and b are standard deviations determined from three or four independent experiments. (c) Dependence of the normalized, total, and individual relaxation amplitudes, A_T (▲), A₁ (■), and A₂ (□), of CTP hydrolysis by a single, noninteracting site of the DnaB helicase, in buffer T4, in the presence of dC-(pC)₉(pA)₁₀, on the total concentration of the enzyme (protomer). The solid lines are nonlinear, least-squares fits according to the three-step sequential mechanism of CTP hydrolysis, described by Scheme 1. The rate constants, obtained from the fits of the relaxation times and the amplitude, are included in Table 1.

(a) Time course of CTP hydrolysis by a single, noninteracting site of the DnaB helicase hexamer in single-turnover experiments (large excess of the enzyme over CTP), in buffer T4. The produced CDP is shown as a fraction of the total concentration of CTP in the sample. The concentrations of the cofactor and the enzyme were 1.9 × 10⁻⁷ M and 7.5 × 10⁻⁶ M (protomer), respectively. The solid line is the nonlinear least-squares fit of the double-exponential function (eq 1) to the experimental kinetic curve. The dashed line is the nonlinear least-squares fit, obtained using a single-exponential function (eq 1) (details in the text). (b) Dependence of the reciprocal of the relaxation time, 1/τ₁, for CTP hydrolysis by the single, noninteracting site of the DnaB helicase in buffer T4, on the total concentration of the enzyme (protomer). The solid line is a numerical, nonlinear least-squares fit of the expenmental data to the three-step sequential mechanism, defined by Scheme 1. (c) Dependence of the reciprocal of the relaxation time, 1/τ₂, for CTP hydrolysis by the single, noninteracting site of the DnaB helicase in buffer T4, on the total concentration of the enzyme (protomer). The solid line is a numericnl, nonlinear least-squares fit of the experimental data to the three-step sequential mechanism, defined by Scheme 1. The error bars in panels b and c are standard deviations determined in three or four independent experiments. (d) Dependence of the normalized total and individual relaxation amplitudes, A_T (▲), A₁ (■), and A₂ (□), of CTP hydrolysis by a single, noninteracting site of the DnaB helicase in buffer T4 on the total concentration of the enzyme (protomer). The solid lines are nonlinear least-squares fits according to the three-step sequential mechanism of ATP hydrolysis in the noninteracting site of the helicase, described by Scheme 1. The rate constants, obtained from the fits of the relaxation times and the amplitudes, are included in Table 1.

(a) Dependence of the partial equilibrium constants, characterizing the equilibria between the intermediates of the ATP hydrolysis reaction by the single, noninteracting site of the DnaB helicase, on the reciprocal of the temperature (kelvin) (van’t Hoff plots): K₁ (■), K₂ (□), and K₃ (▲). (b) Dependence of the partial equilibrium constants, characterizing the equilibria between the intermediates of the CTP hydrolysis reaction by the single, noninteracting site of the DnaB helicase, on the reciprocal of the temperature (kelvin) (van’t Hoff plots): K₁ (■), K₂ (□), and K₃ (▲). The obtained values of corresponding enthalpy and entropy changes are included in Table 2.

(a) Time course of ATP hydrolysis by a single, noninteracting site of the DnaB helicase hexamer in the presence of the ssDNA 20-mer, dA(pA)₁₉ (□), in single-turnover experiments, in buffer T4. The produced ADP is shown as a fraction of the total concentration of the ATP in the sample. The concentrations of the cofactor and the enzyme were 1.9 × 10⁻⁷ M and 7.5 × 10⁻⁶ M (protomer), respectively. The concentration of the nucleic acid was 6.5 × 10⁻⁵ M (oligomer). For the sake of comparison, the time course of ATP hydrolysis by a single, noninteracting site of the DnaB helicase hexamer in the absence of the ssDNA 20-mer is included in panel a, obtained at the same cofactor and enzyme concentrations (■). The solid line is the nonlinear least-squares fit of the double-exponential function (eq 1) to the experimental curve (details in text). (b) Dependence of the reciprocal of the relaxation time, 1/τ₂, for ATP hydrolysis by the single, noninteracting site of the DnaB helicase, in the presence of dA (pA)₁₉ upon the total concentration of the enzyme (protomer). The solid line is a numerical, nonlinear least-squares fit of the experimental data to the three-step sequential mechanism, defined by Scheme 1. (c) Dependence of the normalized total and individual relaxation amplitudes, A_T (▲), A₁ (■), and A₂ (□), of ATP hydrolysis by a single, noninteracting site of the DnaB helicase, in the presence of dA(pA)₁₉, on the logarithm of the total concentration of the enzyme (protomer). The solid lines are nonlinear least-squares fits according to the three-step sequential mechanism of ATP hydrolysis in the noninteracting site of the helicase, described by Scheme 1. The rate constants, obtained from the fits of the relaxation times and the amplitudes, are included in Table 1.

(a) Time course of CTP hydrolysis by a single, noninteracting site of the DnaB helicase hexamer in the presence of the ssDNA 20-mer, dA(pA)₁₉ (□), in single-turnover experiments, in buffer T4. The produced CDP is shown as a fraction of the total concentration of CTP in the sample. The concentrations of the cofactor and the enzyme were 1.9 × 10⁻⁷ M and 7.5 × 10⁻⁶ M (protomer), respectively. The concentration of the nucleic acid was 6.5 × 10⁻⁵ M (oligomer). For the sake of comparison, the time course of CTP hydrolysis by a single, noninteracting site of the DnaB belicase hexamer, in the absence of the ssDNA 20-mer, is included in panel a, at the same cofactor and enzyme concentrations (■). The solid line is the nonlinear least-squares fit of the double-exponential function (eq 1) to the experimental curve. (b) Dependence of the reciprocal of the relaxation time, l/τ₁, for CTP hydrolysis by the single, noninteracting site of the DnaB helicase in buffer T4, in the presence of dA(pA)₁₉, on the total concentration of the enzyme (protomer). The solid line is a numerical, nonlinear, least-squares fit of the experimental data to the three-step sequential mechanism, defined by Scheme 1. (c) Dependence of the reciprocal of the relaxation time, 1/τ₂, for CIP hydrolysis by the single, noninteracting site of the DnaB helicase in buffer T4, in the presence of dA(pA)₁₉, on the total concentration of the enzyme (protomer). The solid line is a numerical, nonlinear, least-squares fit of the experimental data to the three-step sequential mechanism, defined by Scheme 1. The error bars in panels b and c are standard deviations determined in three or four independent experiments. (d) Dependence of the normalized, total, and individual relaxation amplitudes, A_T (▲), A₁ (■), and A₂ (□), respectively, of CTP hydrolysis by a single, noninteracting site of the DnaB helicase in buffer T4, in the presence of dA(pA)₁₉, on the total concentration of the enzyme (protomer). The solid lines are nonlinear, least-squares fits according to the three-step sequential mechanism of CTP hydrolysis in the noninteracting site of the helicase, described by Scheme 1. The rate constants, obtained from the fits of the relaxation times and the amplitudes, are included in Table 1.

Fluorescence titrations (λ_ex = 325 nm; λ_em = 410 nm)of the etheno derivative of the ssDNA 20-mers, dεA(pεA)₁₉ (O), dεA (pεA)₉(pT)₁₀ (■), and dT(pT)₉(pεA)₁₀ (□), with the DnaB helicase in buffer T4 (pH 8.1 and 20 °C). The concentration of all ssDNA oligomers was 4.5 × 10⁻⁷ M (oligomer). The solid lines are nonlinear, least-squares fits of the titration curves to a single-binding site isotherm (eq 3) with two fitting parameters: K = 1.5 × 10⁷ M⁻¹ and ΔF_max =2.6 (○); K = 8 × 10⁶ M⁻¹, and ΔF_max =0.85 (■); K = 1.1 × 10⁷ M⁻¹, and ΔF_max = 1.0 (□).

(a) Dependence of the reciprocal of the relaxation time, 1/τ₂, for CTP hydrolysis by the single, noninteracting site of the DnaB helicase, in the presence of dA(pA)₉(pC)₁₀, on the total concentration of the enzyme (protomer). The solid line is a nonlinear, least-squares fit of the experimental data to the three-step sequential mechanism, defined by Scheme 1. (b) Dependence of the normalized, total, and individual relaxation amplitudes, A_T (▲), A₁ (■), and A₂ (□), of CTP hydrolysis by a single, noninteracting site of the DnaB helicase, in the presence of dA(pA)₉(pC)₁₀, on the concentration of the enzyme (protomer). The solid lines are nonlinear, least-squares fits according to the three-step sequential mechanism of CTP hydrolysis, described by Scheme 1. The rate constants, obtained from the fits of the relaxation times and the amplitudes, are included in Table 1.

The simplest mechanism of the CTP hydrolysis by the DnaB helicase, which can account for the observed experimental behavior, is, in general, described by Scheme 1 A bimolecular association of the cofactor with the active site of one of the DnaB subunits (H + CTP ↔ H-CTP) is followed by two reversible first-order transitions, the CTP hydrolysis [H-CTP ↔ (H-CDP·P_i)₁] and the isomerization of the helicase–product complex [(H-CDP·P_i)₁ ↔ (H-CDP·P_i)₂] (31). Thus, the major aspects of the kinetic mechanism of the pyrimidine cofactor hydrolysis, CTP, are the same as the main features of the ATP kinetic mechanism (31). The solid lines in panels b–d of Figure 1b are nonlinear least-squares fits of the relaxation times and amplitudes according to the proposed mechanism (Scheme 1). The analyses were first performed by numerical, nonlinear least-squares fitting of the individual relaxation times and amplitudes, using the matrix projection operator approach (40). Simultaneous, global fitting of both the relaxation times and the amplitudes then refined the values of the rate constants. The obtained rate and equilibrium constants are included in Table 1.