Biomedical subjects

S C Kou

Publications and source records attributed to S C Kou.

10 recordsLinked to original sources

PubMed2006

When does the Michaelis-Menten equation hold for fluctuating enzymes?

Enzymes are dynamic entities: both their conformation and catalytic activity fluctuate over time. When such fluctuations are relatively fast, it is not surprising that the classical Michaelis-Menten (MM) relationship between the steady-state enzymatic velocity and the substrate concentration still holds. However, recent single-molecule experiments have shown that this is the case even for an enzyme whose catalytic activity fluctuates on the 10(-4)-10 s range. The purpose of this paper is to examine various scenarios in which slowly fluctuating enzymes would still obey the MM relationship. Specifically, we consider (1) the quasi-static condition (e.g., the conformational fluctuation of the enzyme-substrate complex is much slower than binding, catalysis, and the conformational fluctuations of the free enzyme), (2) the quasi-equilibrium condition (when the substrate dissociation is much faster than catalysis, irrespective of the time scales or amplitudes of conformational fluctuations), and (3) the conformational-equilibrium condition (when the dissociation and catalytic rates depend on the conformational coordinate in the same way). For each of these scenarios, the physical meaning of the apparent Michaelis constant and catalytic rate constant is provided. Finally, as an example, the theoretical analysis of a recent single-molecule enzyme assay is considered in light of the perspectives presented in this paper.

Biophysics↗

PubMed2006

A study of density of states and ground states in hydrophobic-hydrophilic protein folding models by equi-energy sampling.

We propose an equi-energy (EE) sampling approach to study protein folding in the two-dimensional hydrophobic-hydrophilic (HP) lattice model. This approach enables efficient exploration of the global energy landscape and provides accurate estimates of the density of states, which then allows us to conduct a detailed study of the thermodynamics of HP protein folding, in particular, on the temperature dependence of the transition from folding to unfolding and on how sequence composition affects this phenomenon. With no extra cost, this approach also provides estimates on global energy minima and ground states. Without using any prior structural information of the protein the EE sampler is able to find the ground states that match the best known results in most benchmark cases. The numerical results demonstrate it as a powerful method to study lattice protein folding models.

Algorithms↗

PubMed2005

Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited.

Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at the single-molecule level. We monitored long time traces of enzymatic turnovers for individual beta-galactosidase molecules by detecting one fluorescent product at a time. A molecular memory phenomenon arises at high substrate concentrations, characterized by clusters of turnover events separated by periods of low activity. Such memory lasts for decades of timescales ranging from milliseconds to seconds owing to the presence of interconverting conformers with broadly distributed lifetimes. We proved that the Michaelis-Menten equation still holds even for a fluctuating single enzyme, but bears a different microscopic interpretation.

Catalysis↗

PubMed2005

Single-molecule Michaelis-Menten equations.

This paper summarizes our present theoretical understanding of single-molecule kinetics associated with the Michaelis-Menten mechanism of enzymatic reactions. Single-molecule enzymatic turnover experiments typically measure the probability density f(t) of the stochastic waiting time t for individual turnovers. While f(t) can be reconciled with ensemble kinetics, it contains more information than the ensemble data; in particular, it provides crucial information on dynamic disorder, the apparent fluctuation of the catalytic rates due to the interconversion among the enzyme's conformers with different catalytic rate constants. In the presence of dynamic disorder, f(t) exhibits a highly stretched multiexponential decay at high substrate concentrations and a monoexponential decay at low substrate concentrations. We derive a single-molecule Michaelis-Menten equation for the reciprocal of the first moment of f(t), 1/ , which shows a hyperbolic dependence on the substrate concentration [S], similar to the ensemble enzymatic velocity. We prove that this single-molecule Michaelis-Menten equation holds under many conditions, in particular when the intercoversion rates among different enzyme conformers are slower than the catalytic rate. However, unlike the conventional interpretation, the apparent catalytic rate constant and the apparent Michaelis constant in this single-molecule Michaelis-Menten equation are complicated functions of the catalytic rate constants of individual conformers. We also suggest that the randomness parameter r, defined as <(t - )2> / t2, can serve as an indicator for dynamic disorder in the catalytic step of the enzymatic reaction, as it becomes larger than unity at high substrate concentrations in the presence of dynamic disorder.

Algorithms↗

PubMed2005

Observation of a power-law memory kernel for fluctuations within a single protein molecule.

The fluctuation of the distance between a fluorescein-tyrosine pair within a single protein complex was directly monitored in real time by photoinduced electron transfer and found to be a stationary, time-reversible, and non-Markovian Gaussian process. Within the generalized Langevin equation formalism, we experimentally determine the memory kernel K(t), which is proportional to the autocorrelation function of the random fluctuating force. K(t) is a power-law decay, t(-0.51 +/- 0.07) in a broad range of time scales (10(-3)-10 s). Such a long-time memory effect could have implications for protein functions.

Antibodies, Monoclonal↗

PubMed2005

Fluctuating enzymes: lessons from single-molecule studies.

Recent single-molecule enzymology measurements with improved statistics have demonstrated that a single enzyme molecule exhibits large temporal fluctuations of the turnover rate constant at a broad range of time scales (from 1 ms to 100 s). The rate constant fluctuations, termed as dynamic disorder, are associated with fluctuations of the protein conformations observed on the same time scales. We discuss the unique information extractable from these experiments and the reconciliation of these observations with ensemble-averaged Michaelis-Menten equation. A theoretical model based on the generalized Langevin equation (GLE) treatment of Kramers' barrier crossing problem for chemical reactions accounts naturally for the observation of dynamic disorder and highly dispersed kinetics.

Enzymes↗

PubMed2005

Nonequilibrium steady state of a nanometric biochemical system: determining the thermodynamic driving force from single enzyme turnover time traces.

A single enzyme molecule in a living cell is a nanometric system that catalyzes biochemical reactions in a nonequilibrium steady-state condition. The chemical driving force, Deltamu, is an important thermodynamic quantity that determines the extent to which the reaction system is away from equilibrium. Here we show that Deltamu for an enzymatic reaction in situ can be determined from the nonequilibrium time traces for enzymatic turnovers of individual enzyme molecules, which can now be recorded experimentally by single-molecule techniques. Three different Deltamu estimators are presented from principles of nonequilibrium statistical mechanics: fluctuation theorem, Kawasaki identity, and fluctuation dissipation theorem, respectively. In particular, a maximum likelihood estimation method of Deltamu has been derived based on fluctuation theorem. The statistical precisions of these three Deltamu estimators are analyzed and compared for experimental time traces with finite lengths.

Computer Simulation↗

PubMed2004

Generalized Langevin equation with fractional Gaussian noise: subdiffusion within a single protein molecule.

By introducing fractional Gaussian noise into the generalized Langevin equation, the subdiffusion of a particle can be described as a stationary Gaussian process with analytical tractability. This model is capable of explaining the equilibrium fluctuation of the distance between an electron transfer donor and acceptor pair within a protein that spans a broad range of time scales, and is in excellent agreement with a single-molecule experiment.

FMN Reductase↗

PubMed2000

Diagnostic usefulness of telomerase activity in nasopharyngeal carcinoma.

Telomeres are specialized structures at the ends of eukaryotic chromosomes which are composed of simple repetitive G-rich hexameric sequences. Activation of telomerase, a ribonucleoprotein that synthesizes telomeric DNA, is found in most malignant tumors. However, little data is available concerning the correlation between telomerase activity and NPC (nasopharyngeal carcinoma). In this study, telomerase activation was determined using the TRAP (telomerase repeat amplification protocol) assay in 62 nasopharyngeal biopsies (25 NPC, 25 non-malignant nasopharyngeal lymphoid tissues, 12 post-irradiated nasopharyngeal tissues). The results showed that strong telomerase activity was present in both NPC and non-malignant nasopharyngeal biopsies. Post-irradiated nasopharyngeal samples had a significantly lower telomerase activity than NPC and non-malignant nasopharyngeal lymphoid tissues. It is well known that nasopharyngeal tissue is infiltrated by numerous lymphocytes, which might retain telomerase activity. Therefore, the finding that the telomerase activation was lowest in post-irradiated nasopharyngeal tissues is reasonable because of the destruction of activated lymphocytes and NPC by radiation. NPC biopsies with positive lymph node involvement exhibited higher levels of telomerase compared to those without lymph node involvement. Our data indicate a positive association between telomerase activity and tumor potential for lymphatic spreading in limited local tumors. In addition, telomerase activity may be useful as a diagnostic marker in the detection of tumor cells in recurrent NPC, but not in primary NPC.

Adolescent↗

PubMed1970

Galactose transport in Saccharomyces cerevisiae. II. Characteristics of galactose uptake and exchange in galactokinaseless cells.

The characteristics of the inducible galactose system in Saccharomyces cerevisiae were studied by using the nonmetabolized galactose analogues, l-arabinose and d-fucose, and galactokinaseless and transportless mutants. Induced wild-type cells transport l-arabinose by facilitated diffusion. Transportless cells transport neither galactose nor l-arabinose above the noninduced rate, whereas galactokinaseless cells transport galactose l-arabinose and d-fucose by facilitated diffusion. Determination of unidirectional rate of (14)C-labeled galactose uptake by preloaded galactokinaseless cells, containing a large unlabeled free-galactose pool, showed that the rate of galactose uptake by facilitated diffusion is greater than the rate of galactose metabolism at similar external galactose concentrations.

Arabinose↗