Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes

Enyzme kinetics are cyclic. We study a Markov renewal process model of single-enzyme turnover in nonequilibrium steady-state (NESS) with sustained concentrations for substrates and products. We show that the forward and backward cycle times have idential non-exponential distributions: \QQ_+(t)=\QQ_-(t). This equation generalizes the Haldane relation in reversible enzyme kinetics. In terms of the probabilities for the forward ($p_+$) and backward ($p_-$) cycles, $k_BT\ln(p_+/p_-)$ is shown to be the chemical driving force of the NESS, $\Delta\mu$. More interestingly, the moment generating function of the stochastic number of substrate cycle $\nu(t)$, follows the fluctuation theorem in the form of Kurchan-Lebowitz-Spohn-type symmetry. When $\lambda$ = $\Delta\mu/k_BT$, we obtain the Jarzynski-Hatano-Sasa-type equality: $\equiv$ 1 for all $t$, where $\nu\Delta\mu$ is the fluctuating chemical work done for sustaining the NESS. This theory suggests possible methods to experimentally determine the nonequilibrium driving force {\it in situ} from turnover data via single-molecule enzymology.Comment: 4 pages, 3 figure

Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations

Using a one-dimensional macromolecule in aqueous solution as an illustration, we demonstrate that the relative entropy from information theory, $\sum_k p_k\ln(p_k/p_k^*)$, has a natural role in the energetics of equilibrium and nonequilibrium conformational fluctuations of the single molecule. It is identified as the free energy difference associated with a fluctuating density in equilibrium, and is associated with the distribution deviate from the equilibrium in nonequilibrium relaxation. This result can be generalized to any other isothermal macromolecular systems using the mathematical theories of large deviations and Markov processes, and at the same time provides the well-known mathematical results with an interesting physical interpretations.Comment: 5 page

Exotic mesons from quantum chromodynamics with improved gluon and quark actions on the anisotropic lattice

Hybrid (exotic) mesons, which are important predictions of quantum chromodynamics (QCD), are states of quarks and anti-quarks bound by excited gluons. First principle lattice study of such states would help us understand the role of ``dynamical'' color in low energy QCD and provide valuable information for experimental search for these new particles. In this paper, we apply both improved gluon and quark actions to the hybrid mesons, which might be much more efficient than the previous works in reducing lattice spacing error and finite volume effect. Quenched simulations were done at $\beta=2.6$ and on a $\xi=3$ anisotropic $12^3\times36$ lattice using our PC cluster. We obtain $2013 \pm 26 \pm 71$ MeV for the mass of the $1^{-+}$ hybrid meson ${\bar q}qg$ in the light quark sector, and $4369 \pm 37 \pm 99$Mev in the charm quark sector; the mass splitting between the $1^{-+}$ hybrid meson ${\bar c}c g$ in the charm quark sector and the spin averaged S-wave charmonium mass is estimated to be $1302 \pm 37 \pm 99$ MeV. As a byproduct, we obtain $1438 \pm 32 \pm 57$ MeV for the mass of a P-wave $1^{++}$ ${\bar u}u$ or ${\bar d}d$ meson and $1499 \pm 28 \pm 65$ MeV for the mass of a P-wave $1^{++}$ ${\bar s}s$ meson, which are comparable to their experimental value 1426 MeV for the $f_1(1420)$ meson. The first error is statistical, and the second one is systematical. The mixing of the hybrid meson with a four quark state is also discussed.Comment: 12 pages, 3 figures. Published versio

COMPUTER SIMULATION OF "SPLASH CONTROL IN COMPETITIVE DIVING

The purpose of the study was to examine the relationship between the hand pattern and the water splash height during a diver's entry using a computer simulation method. A physical and mathematical model of the impact of a wedged solid object with an ideal fluid was developed. The motion equation (interaction function of solid and fluid) of the solid was established with satisfaction of control functions and initial boundary conditions of the fluid. A finite element method was used to simulate the impact process, with the wedge angle changed from 4" to 80- during the impact. The results suggested that the fluid splash height is inversely proportional to the wedge angle. The "splash control" technique derived from the simulation was also applied in training professional divers and positive results were obtained

The Dynamics of Zeroth-Order Ultrasensitivity: A Critical Phenomenon in Cell Biology

It is well known since the pioneering work of Goldbeter and Koshland [Proc. Natl. Acad. Sci. USA, vol. 78, pp. 6840-6844 (1981)] that cellular phosphorylation- dephosphorylation cycle (PdPC), catalyzed by kinase and phosphatase under saturated condition with zeroth order enzyme kinetics, exhibits ultrasensitivity, sharp transition. We analyse the dynamics aspects of the zeroth order PdPC kinetics and show a critical slowdown akin to the phase transition in condensed matter physics. We demonstrate that an extremely simple, though somewhat mathematically "singular" model is a faithful representation of the ultrasentivity phenomenon. The simplified mathematical model will be valuable, as a component, in developing complex cellular signaling network theory as well as having a pedagogic value.Comment: 8 pages, 3 figure