33,938 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
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
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
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
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
Human African trypanosomiasis : the current situation in endemic regions and the risks for non-endemic regions from imported cases
Human African trypanosomiasis (HAT) is caused by Trypanosoma brucei
gambiense and T. b. rhodesiense and caused devastating epidemics during the 20th
century. Due to effective control programs implemented in the last two decades, the
number of reported cases has fallen to a historically low level. Although fewer than
977 cases were reported in 2018 in endemic countries, HAT is still a public health
problem in endemic regions until it is completely eliminated. In addition, almost 150
confirmed HAT cases were reported in non-endemic countries in the last three
decades. The majority of non-endemic HAT cases were reported in Europe, United
States and South Africa, due to historical alliances, economic links or geographic
proximity to disease endemic countries. Furthermore, with the implementation of the
“Belt and Road” project, sporadic imported HAT cases have been reported in China
as a warning sign of tropical diseases prevention. In this paper, we explore and
interpret the data on HAT incidence and find no positive correlation between the
number of HAT cases from endemic and non-endemic countries.This data will
provide useful information for better understanding the imported cases of HAT
globally in the post-elimination phase
Exchange and correlation near the nucleus in density functional theory
The near nucleus behavior of the exchange-correlation potential in Hohenberg-Kohn-Sham density functional theory is investigated. It is
shown that near the nucleus the linear term of of the spherically
averaged exchange-correlation potential is nonzero, and that
it arises purely from the difference between the kinetic energy density at the
nucleus of the interacting system and the noninteracting Kohn-Sham system. An
analytical expression for the linear term is derived. Similar results for the
exchange and correlation potentials are also
obtained separately. It is further pointed out that the linear term in
arising mainly from is rather small, and
therefore has a nearly quadratic structure near the nucleus.
Implications of the results for the construction of the Kohn-Sham system are
discussed with examples.Comment: 10 page
Formation of helical states in wormlike polymer chains
We propose a potential for wormlike polymer chains which can be used to model
the low-temperature conformational structures. We successfully reproduced helix
ground states up to 6.5 helical loops, using the multicanonical Monte Carlo
simulation method. We demonstrate that the coil-helix transition involves four
distinct phases: coil(gaslike), collapsed globular(liquidlike), and two helical
phases I and II (both solidlike). The helix I phase is characterized by a
helical structure with dangling loose ends, and the helix II phase corresponds
to a near perfect helix ordering in the entire crystallized chain.Comment: 5 pages, 2 figures, Submitted to PR
Toolbox for analyzing finite two-state trajectories
In many experiments, the aim is to deduce an underlying multi-substate on-off
kinetic scheme (KS) from the statistical properties of a two-state trajectory.
However, the mapping of a KS into a two-state trajectory leads to the loss of
information about the KS, and so, in many cases, more than one KS can be
associated with the data. We recently showed that the optimal way to solve this
problem is to use canonical forms of reduced dimensions (RD). RD forms are
on-off networks with connections only between substates of different states,
where the connections can have non-exponential waiting time probability density
functions (WT-PDFs). In theory, only a single RD form can be associated with
the data. To utilize RD forms in the analysis of the data, a RD form should be
associated with the data. Here, we give a toolbox for building a RD form from a
finite two-state trajectory. The methods in the toolbox are based on known
statistical methods in data analysis, combined with statistical methods and
numerical algorithms designed specifically for the current problem. Our toolbox
is self-contained - it builds a mechanism based only on the information it
extracts from the data, and its implementation on the data is fast (analyzing a
10^6 cycle trajectory from a thirty-parameter mechanism takes a couple of hours
on a PC with a 2.66 GHz processor). The toolbox is automated and is freely
available for academic research upon electronic request
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