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

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

Stochastic Physics, Complex Systems and Biology

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated equilibrium, spontaneous random "mutations" and "adaptations". On an evlutionary time scale it produces sustainable diversity among individuals in a homogeneous population rather than convergence as usually predicted by a deterministic dynamics. The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a perspective.Comment: 10 page

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

The Spin Mass of an Electron Liquid

We show that in order to calculate correctly the {\it spin current} carried by a quasiparticle in an electron liquid one must use an effective "spin mass" $m_s$, that is larger than both the band mass, $m_b$, which determines the charge current, and the quasiparticle effective mass $m^*$, which determines the heat capacity. We present microscopic calculations of $m_s$ in a paramagnetic electron liquid in three and two dimensions, showing that the mass enhancement $m_s/m_b$ can be a very significant effect.Comment: 10 pages, 1 figur

Compression of Atomic Phase Space Using an Asymmetric One-Way Barrier

We show how to construct asymmetric optical barriers for atoms. These barriers can be used to compress phase space of a sample by creating a confined region in space where atoms can accumulate with heating at the single photon recoil level. We illustrate our method with a simple two-level model and then show how it can be applied to more realistic multi-level atoms

Circadian and Ultradian Rhythms of Free Glucocorticoid Hormone Are Highly Synchronized between the Blood, the Subcutaneous Tissue, and the Brain

Total glucocorticoid hormone levels in plasma of various species, including humans, follow a circadian rhythm that is made up from an underlying series of hormone pulses. In blood most of the glucocorticoid is bound to corticosteroid-binding globulin and albumin, resulting in low levels of free hormone. Although only the free fraction is biologically active, surprisingly little is known about the rhythms of free glucocorticoid hormones. We used single-probe microdialysis to measure directly the free corticosterone levels in the blood of freely behaving rats. Free corticosterone in the blood shows a distinct circadian and ultradian rhythm with a pulse frequency of approximately one pulse per hour together with an increase in hormone levels and pulse height toward the active phase of the light/dark cycle. Similar rhythms were also evident in the subcutaneous tissue, demonstrating that free corticosterone rhythms are transferred from the blood into peripheral target tissues. Furthermore, in a dual-probe microdialysis study, we demonstrated that the circadian and ultradian rhythms of free corticosterone in the blood and the subcutaneous tissue were highly synchronized. Moreover, free corticosterone rhythms were also synchronous between the blood and the hippocampus. These data demonstrate for the first time an ultradian rhythm of free corticosterone in the blood that translates into synchronized rhythms of free glucocorticoid hormone in peripheral and central tissues. The maintenance of ultradian rhythms across tissue barriers in both the periphery and the brain has important implications for research into aberrant biological rhythms in disease and for the development of improved protocols for glucocorticoid therapy