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

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

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.

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 $L$-mers, the number of these candidates grows only as $L^2$. 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