33,957 research outputs found
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, , 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
Relationship between Thermodynamic Driving Force and One-Way Fluxes in Reversible Chemical Reactions
Chemical reaction systems operating in nonequilibrium open-system states
arise in a great number of contexts, including the study of living organisms,
in which chemical reactions, in general, are far from equilibrium. Here we
introduce a theorem that relates forward and re-verse fluxes and free energy
for any chemical process operating in a steady state. This rela-tionship, which
is a generalization of equilibrium conditions to the case of a chemical process
occurring in a nonequilibrium steady state, provides a novel equivalent
definition for chemical reaction free energy. In addition, it is shown that
previously unrelated theories introduced by Ussing and Hodgkin and Huxley for
transport of ions across membranes, Hill for catalytic cycle fluxes, and Crooks
for entropy production in microscopically reversible systems, are united in a
common framework based on this relationship.Comment: 11 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
() and backward () cycles, is shown to be the
chemical driving force of the NESS, . More interestingly, the moment
generating function of the stochastic number of substrate cycle ,
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:
1 for all , where 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
Liquid-gas Phase Transition in Strange Hadronic Matter with Weak Y-Y Interaction
The liquid-gas phase transition in strange hadronic matter is reexamined by
using the new parameters about the interaction deduced from
recent observation of double hypernucleus. The
extended Furnstahl-Serot-Tang model with nucleons and hyperons is utilized. The
binodal surface, the limit pressure, the entropy, the specific heat capacity
and the Caloric curves are addressed. We find that the liquid-gas phase
transition can occur more easily in strange hadronic matter with weak Y-Y
interaction than that of the strong Y-Y interaction.Comment: 10 pages, 7 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
Excluded-Volume Effects in Tethered-Particle Experiments: Bead Size Matters
The tethered-particle method is a single-molecule technique that has been
used to explore the dynamics of a variety of macromolecules of biological
interest. We give a theoretical analysis of the particle motions in such
experiments. Our analysis reveals that the proximity of the tethered bead to a
nearby surface (the microscope slide) gives rise to a volume-exclusion effect,
resulting in an entropic force on the molecule. This force stretches the
molecule, changing its statistical properties. In particular, the proximity of
bead and surface brings about intriguing scaling relations between key
observables (statistical moments of the bead) and parameters such as the bead
size and contour length of the molecule. We present both approximate analytic
solutions and numerical results for these effects in both flexible and
semiflexible tethers. Finally, our results give a precise,
experimentally-testable prediction for the probability distribution of the
distance between the polymer attachment point and the center of the mobile
bead.Comment: 4 pages, 3 figure
Discerning Aggregation in Homogeneous Ensembles: A General Description of Photon Counting Spectroscopy in Diffusing Systems
In order to discern aggregation in solutions, we present a quantum mechanical
analog of the photon statistics from fluorescent molecules diffusing through a
focused beam. A generating functional is developed to fully describe the
experimental physical system as well as the statistics. Histograms of the
measured time delay between photon counts are fit by an analytical solution
describing the static as well as diffusing regimes. To determine empirical
fitting parameters, fluorescence correlation spectroscopy is used in parallel
to the photon counting. For expedient analysis, we find that the distribution's
deviation from a single Poisson shows a difference between two single fluor
moments or a double fluor aggregate of the same total intensities. Initial
studies were performed on fixed-state aggregates limited to dimerization.
However preliminary results on reactive species suggest that the method can be
used to characterize any aggregating system.Comment: 30 pages, 5 figure
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