2,549 research outputs found
Dynamical fluctuations in biochemical reactions and cycles
We develop theory for the dynamics and fluctuations in some cyclic and linear biochemical reactions. We use the approach of maximum caliber, which computes the ensemble of paths taken by the system, given a few experimental observables. This approach may be useful for interpreting single-molecule or few-particle experiments on molecular motors, enzyme reactions, ion-channels, and phosphorylation-driven biological clocks. We consider cycles where all biochemical states are observable. Our method shows how: (1) the noise in cycles increases with cycle size and decreases with the driving force that spins the cycle and (2) provides a recipe for estimating small-number features, such as probability of backward spin in small cycles, from experimental data. The back-spin probability diminishes exponentially with the deviation from equilibrium. We believe this method may also be useful for other few-particle nonequilibrium biochemical reaction systems
Model for Folding and Aggregation in RNA Secondary Structures
We study the statistical mechanics of RNA secondary structures designed to
have an attraction between two different types of structures as a model system
for heteropolymer aggregation. The competition between the branching entropy of
the secondary structure and the energy gained by pairing drives the RNA to
undergo a `temperature independent' second order phase transition from a molten
to an aggregated phase'. The aggregated phase thus obtained has a
macroscopically large number of contacts between different RNAs. The partition
function scaling exponent for this phase is \theta ~ 1/2 and the crossover
exponent of the phase transition is \nu ~ 5/3. The relevance of these
calculations to the aggregation of biological molecules is discussed.Comment: Revtex, 4 pages; 3 Figures; Final published versio
Determine the Potential Drill Utilization Improvements and Rock Fragmentation Requirements Using Directional Drilling in a Coal Mining Overburden Highwall Application
This project analyzed the efficiency of incorporating the use of directional drilling technology into coal overburden blasting. Directional drilling is currently in use in the petroleum industry and it is believed that it will be a valuable asset in the mining industry. This project has shown that directional drilling can be a viable technology for use in the coal overburden removal process resulting in increased drill utilization and potential for cost savings. Future work regarding blasting and geotechnical evaluation should be performed to solidify the concept
Nonuniversal power law scaling in the probability distribution of scientific citations
We develop a model for the distribution of scientific citations. The model
involves a dual mechanism: in the direct mechanism, the author of a new paper
finds an old paper A and cites it. In the indirect mechanism, the author of a
new paper finds an old paper A only via the reference list of a newer
intermediary paper B, which has previously cited A. By comparison to citation
databases, we find that papers having few citations are cited mainly by the
direct mechanism. Papers already having many citations ('classics') are cited
mainly by the indirect mechanism. The indirect mechanism gives a power-law
tail. The 'tipping point' at which a paper becomes a classic is about 21
citations for papers published in the Institute for Scientific Information
(ISI) Web of Science database in 1981, 29 for Physical Review D papers
published from 1975-1994, and 39 for all publications from a list of high
h-index chemists assembled in 2007. The power-law exponent is not universal.
Individuals who are highly cited have a systematically smaller exponent than
individuals who are less cited.Comment: 7 pages, 3 figures, 2 table
A Bell-Evans-Polanyi principle for molecular dynamics trajectories and its implications for global optimization
The Bell-Evans-Polanyi principle that is valid for a chemical reaction that
proceeds along the reaction coordinate over the transition state is extended to
molecular dynamics trajectories that in general do not cross the dividing
surface between the initial and the final local minima at the exact transition
state. Our molecular dynamics Bell-Evans-Polanyi principle states that low
energy molecular dynamics trajectories are more likely to lead into the basin
of attraction of a low energy local minimum than high energy trajectories. In
the context of global optimization schemes based on molecular dynamics our
molecular dynamics Bell-Evans-Polanyi principle implies that using low energy
trajectories one needs to visit a smaller number of distinguishable local
minima before finding the global minimum than when using high energy
trajectories
Heteropolymer Sequence Design and Preferential Solvation of Hydrophilic Monomers: One More Application of Random Energy Model
In this paper, we study the role of surface of the globule and the role of
interactions with the solvent for designed sequence heteropolymers using random
energy model (REM). We investigate the ground state energy and surface monomer
composition distribution. By comparing the freezing transition in random and
designed sequence heteropolymers, we discuss the effects of design. Based on
our results, we are able to show under which conditions solvation effect
improves the quality of sequence design. Finally, we study sequence space
entropy and discuss the number of available sequences as a function of imposed
requirements for the design quality
Quantification of the differences between quenched and annealed averaging for RNA secondary structures
The analytical study of disordered system is usually difficult due to the
necessity to perform a quenched average over the disorder. Thus, one may resort
to the easier annealed ensemble as an approximation to the quenched system. In
the study of RNA secondary structures, we explicitly quantify the deviation of
this approximation from the quenched ensemble by looking at the correlations
between neighboring bases. This quantified deviation then allows us to propose
a constrained annealed ensemble which predicts physical quantities much closer
to the results of the quenched ensemble without becoming technically
intractable.Comment: 9 pages, 14 figures, submitted to Phys. Rev.
Viscosity Dependence of the Folding Rates of Proteins
The viscosity dependence of the folding rates for four sequences (the native
state of three sequences is a beta-sheet, while the fourth forms an
alpha-helix) is calculated for off-lattice models of proteins. Assuming that
the dynamics is given by the Langevin equation we show that the folding rates
increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and
have a maximum at intermediate values. The Kramers theory of barrier crossing
provides a quantitative fit of the numerical results. By mapping the simulation
results to real proteins we estimate that for optimized sequences the time
scale for forming a four turn \alpha-helix topology is about 500 nanoseconds,
whereas the time scale for forming a beta-sheet topology is about 10
microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at
http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical
Review Letter
Analytical description of finite size effects for RNA secondary structures
The ensemble of RNA secondary structures of uniform sequences is studied
analytically. We calculate the partition function for very long sequences and
discuss how the cross-over length, beyond which asymptotic scaling laws apply,
depends on thermodynamic parameters. For realistic choices of parameters this
length can be much longer than natural RNA molecules. This has to be taken into
account when applying asymptotic theory to interpret experiments or numerical
results.Comment: 10 pages, 13 figures, published in Phys. Rev.
Geometrically Reduced Number of Protein Ground State Candidates
Geometrical properties of protein ground states are studied using an
algebraic approach. It is shown that independent from inter-monomer
interactions, the collection of ground state candidates for any folded protein
is unexpectedly small: For the case of a two-parameter Hydrophobic-Polar
lattice model for -mers, the number of these candidates grows only as .
Moreover, the space of the interaction parameters of the model breaks up into
well-defined domains, each corresponding to one ground state candidate, which
are separated by sharp boundaries. In addition, by exact enumeration, we show
there are some sequences which have one absolute unique native state. These
absolute ground states have perfect stability against change of inter-monomer
interaction potential.Comment: 9 page, 4 ps figures are include
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