Single-Molecule Approach to Enzymology

Abstract

Recent advances in single-molecule enzymology are reviewed. The theoretical underpinning of sincle-molecule enzymatic behaviors is discussed and exemplified by experiements and statistical analyses. In particular, the manifestations of the Michaelis-Menten mechanism, the kinetic scheme with sequential intermediates, and dynamic disorder in single molecule data are presented. A survey of current methods for single molecule enzymatic assays, especially those based on fluorescence detection, is presented as well.

Photostable Single-Molecule Nanoparticle Optical Biosensors for Real-Time Sensing of Single Cytokine Molecules and Their Binding Reactions

“…Notably, we did not observe a digital response (bound/unbound or On/Off) of single molecule reaction of TNFα with MAB, that was supposed to be uniquely associated with single molecule reaction, as predicted and reported using fluorescence detection 48, 49. Even though a single molecule reaction is supposed to occur at a single step as described by quantum mechanics, a complete reaction dynamic process takes several steps, because both molecules need to diffuse together, interact (collide several times) to search for the optimum bind sites, and finally bind.…”

Photostable Single-Molecule Nanoparticle Optical Biosensors for Real-Time Sensing of Single Cytokine Molecules and Their Binding Reactions

“…Notably, we did not observe a digital response (bound/unbound or On/Off) of single molecule reaction of TNFα with MAB, that was supposed to be uniquely associated with single molecule reaction, as predicted and reported using fluorescence detection 48, 49. Even though a single molecule reaction is supposed to occur at a single step as described by quantum mechanics, a complete reaction dynamic process takes several steps, because both molecules need to diffuse together, interact (collide several times) to search for the optimum bind sites, and finally bind.…”

Selective Biomolecular Nanoarrays for Parallel Single-Molecule Investigations

“…34 It is noteworthy that the histogram is well described by a difference of two exponentials (as shown in Figure SI-6); this implies the existence of at least two rate-determining steps in the PvuII-DNA cleavage reaction, consistent with the existence of a Michaelis-Menten complex. 35,36 In addition, our extrapolated value of the overall catalytic rate, or “turnover rate constant”, k, for PvuII (k~1 sec −1 ) is comparable to previously reported values from ensemble measurements under the same buffer conditions (k~0.3 sec −1 ). 37–39 …”

“…By extracting the time delay between when PvuII was first delivered to the nanoarray and when each single-DNA cleavage event was observed, we built a histogram of single-molecule fluorescence extinction as a function of time (Figure b) . It is noteworthy that the histogram is well-described by a difference of two exponentials (as shown in Figure SI-6); this implies the existence of at least two rate-determining steps in the PvuII–DNA cleavage reaction, consistent with the existence of a Michaelis–Menten complex. , In addition, our extrapolated value of the overall catalytic rate constant (i.e., the “turnover rate constant”, k ) for PvuII ( k ≈ 1 s –1 ) is comparable to previously reported values obtained from ensemble measurements under the same buffer conditions ( k ≈ 0.3 s –1 ). − …”

Single-Molecule Electrocatalysis by Single-Walled Carbon Nanotubes

“…The [ S ]-independent nature of ⟨τ on ⟩ −1 can be described by a simple P → PH 2 electro-reduction reaction at a SWNT reactive site (Figure C, reaction (iv)). With the rate constant of this electro-reduction being k 4 red , the probability density function f on (τ) of τ on follows an exponential distribution, , f on (τ) = k 4 red exp(− k 4 red τ); ⟨τ on ⟩ −1 is false⟨ τ on false⟩ − 1 = 1 / ∫ 0 ∞ τ f on ( τ ) d τ = k 4 red Equation 1 is obviously independent of [ S ], consistent with experimental results (Figure A). As P → PH 2 is an electro-reduction reaction, its rate constant k 4 red (and thus ⟨τ on ⟩ −1 ) should be dependent on potential and increases with larger negative potential, as observed experimentally (Figure A).…”

Photostable Single-Molecule Nanoparticle Optical Biosensors for Real-Time Sensing of Single Cytokine Molecules and Their Binding Reactions

“…Notably, we did not observe a digital response (bound/unbound or On/Off) of single molecule reaction of TNFα with MAB, that was supposed to be uniquely associated with single molecule reaction, as predicted and reported using fluorescence detection 48, 49. Even though a single molecule reaction is supposed to occur at a single step as described by quantum mechanics, a complete reaction dynamic process takes several steps, because both molecules need to diffuse together, interact (collide several times) to search for the optimum bind sites, and finally bind.…”

Selective Biomolecular Nanoarrays for Parallel Single-Molecule Investigations

“…34 It is noteworthy that the histogram is well described by a difference of two exponentials (as shown in Figure SI-6); this implies the existence of at least two rate-determining steps in the PvuII-DNA cleavage reaction, consistent with the existence of a Michaelis-Menten complex. 35,36 In addition, our extrapolated value of the overall catalytic rate, or “turnover rate constant”, k, for PvuII (k~1 sec −1 ) is comparable to previously reported values from ensemble measurements under the same buffer conditions (k~0.3 sec −1 ). 37–39 …”

“…By extracting the time delay between when PvuII was first delivered to the nanoarray and when each single-DNA cleavage event was observed, we built a histogram of single-molecule fluorescence extinction as a function of time (Figure b) . It is noteworthy that the histogram is well-described by a difference of two exponentials (as shown in Figure SI-6); this implies the existence of at least two rate-determining steps in the PvuII–DNA cleavage reaction, consistent with the existence of a Michaelis–Menten complex. , In addition, our extrapolated value of the overall catalytic rate constant (i.e., the “turnover rate constant”, k ) for PvuII ( k ≈ 1 s –1 ) is comparable to previously reported values obtained from ensemble measurements under the same buffer conditions ( k ≈ 0.3 s –1 ). − …”

Single-Molecule Electrocatalysis by Single-Walled Carbon Nanotubes

“…The [ S ]-independent nature of ⟨τ on ⟩ −1 can be described by a simple P → PH 2 electro-reduction reaction at a SWNT reactive site (Figure C, reaction (iv)). With the rate constant of this electro-reduction being k 4 red , the probability density function f on (τ) of τ on follows an exponential distribution, , f on (τ) = k 4 red exp(− k 4 red τ); ⟨τ on ⟩ −1 is false⟨ τ on false⟩ − 1 = 1 / ∫ 0 ∞ τ f on ( τ ) d τ = k 4 red Equation 1 is obviously independent of [ S ], consistent with experimental results (Figure A). As P → PH 2 is an electro-reduction reaction, its rate constant k 4 red (and thus ⟨τ on ⟩ −1 ) should be dependent on potential and increases with larger negative potential, as observed experimentally (Figure A).…”

Photostable Single-Molecule Nanoparticle Optical Biosensors for Real-Time Sensing of Single Cytokine Molecules and Their Binding Reactions

“…Notably, we did not observe a digital response (bound/unbound or On/Off) of single molecule reaction of TNFα with MAB, that was supposed to be uniquely associated with single molecule reaction, as predicted and reported using fluorescence detection 48, 49. Even though a single molecule reaction is supposed to occur at a single step as described by quantum mechanics, a complete reaction dynamic process takes several steps, because both molecules need to diffuse together, interact (collide several times) to search for the optimum bind sites, and finally bind.…”

Selective Biomolecular Nanoarrays for Parallel Single-Molecule Investigations

“…34 It is noteworthy that the histogram is well described by a difference of two exponentials (as shown in Figure SI-6); this implies the existence of at least two rate-determining steps in the PvuII-DNA cleavage reaction, consistent with the existence of a Michaelis-Menten complex. 35,36 In addition, our extrapolated value of the overall catalytic rate, or “turnover rate constant”, k, for PvuII (k~1 sec −1 ) is comparable to previously reported values from ensemble measurements under the same buffer conditions (k~0.3 sec −1 ). 37–39 …”

“…By extracting the time delay between when PvuII was first delivered to the nanoarray and when each single-DNA cleavage event was observed, we built a histogram of single-molecule fluorescence extinction as a function of time (Figure b) . It is noteworthy that the histogram is well-described by a difference of two exponentials (as shown in Figure SI-6); this implies the existence of at least two rate-determining steps in the PvuII–DNA cleavage reaction, consistent with the existence of a Michaelis–Menten complex. , In addition, our extrapolated value of the overall catalytic rate constant (i.e., the “turnover rate constant”, k ) for PvuII ( k ≈ 1 s –1 ) is comparable to previously reported values obtained from ensemble measurements under the same buffer conditions ( k ≈ 0.3 s –1 ). − …”

Single-Molecule Electrocatalysis by Single-Walled Carbon Nanotubes

“…The [ S ]-independent nature of ⟨τ on ⟩ −1 can be described by a simple P → PH 2 electro-reduction reaction at a SWNT reactive site (Figure C, reaction (iv)). With the rate constant of this electro-reduction being k 4 red , the probability density function f on (τ) of τ on follows an exponential distribution, , f on (τ) = k 4 red exp(− k 4 red τ); ⟨τ on ⟩ −1 is false⟨ τ on false⟩ − 1 = 1 / ∫ 0 ∞ τ f on ( τ ) d τ = k 4 red Equation 1 is obviously independent of [ S ], consistent with experimental results (Figure A). As P → PH 2 is an electro-reduction reaction, its rate constant k 4 red (and thus ⟨τ on ⟩ −1 ) should be dependent on potential and increases with larger negative potential, as observed experimentally (Figure A).…”