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

Secondary Structures in Long Compact Polymers

Compact polymers are self-avoiding random walks which visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform numerical calculations is generating a sufficiently large number of randomly sampled configurations. We present a Monte-Carlo algorithm which uniformly samples compact polymer configurations in an efficient manner allowing investigations of chains much longer than previously studied. Chain configurations generated by the algorithm are used to compute statistics of secondary structures in compact polymers. We determine the fraction of monomers participating in secondary structures, and show that it is self averaging in the long chain limit and strictly less than one. Comparison with results for lattice models of open polymer chains shows that compact chains are significantly more likely to form secondary structure.Comment: 14 pages, 14 figure

Sequence Heterogeneity Accelerates Protein Search for Targets on DNA

The process of protein search for specific binding sites on DNA is fundamentally important since it marks the beginning of all major biological processes. We present a theoretical investigation that probes the role of DNA sequence symmetry, heterogeneity and chemical composition in the protein search dynamics. Using a discrete-state stochastic approach with a first-passage events analysis, which takes into account the most relevant physical-chemical processes, a full analytical description of the search dynamics is obtained. It is found that, contrary to existing views, the protein search is generally faster on DNA with more heterogeneous sequences. In addition, the search dynamics might be affected by the chemical composition near the target site. The physical origins of these phenomena are discussed. Our results suggest that biological processes might be effectively regulated by modifying chemical composition, symmetry and heterogeneity of a genome.Comment: 10 pages, 5 figure

A lattice model of hydrophobic interactions

Hydrogen bonding is modeled in terms of virtual exchange of protons between water molecules. A simple lattice model is analyzed, using ideas and techniques from the theory of correlated electrons in metals. Reasonable parameters reproduce observed magnitudes and temperature dependence of the hydrophobic interaction between substitutional impurities and water within this lattice.Comment: 7 pages, 3 figures. To appear in Europhysics Letter

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

Microcanonical versus Canonical Analysis of Protein Folding

The microcanonical analysis is shown to be a powerful tool to characterize the protein folding transition and to neatly distinguish between good and bad folders. An off-lattice model with parameter chosen to represent polymers of these two types is used to illustrate this approach. Both canonical and microcanonical ensembles are employed. The required calculations were performed using parallel tempering Monte Carlo simulations. The most revealing features of the folding transition are related to its first-order-like character, namely, the S-bend pattern in the caloric curve, which gives rise to negative microcanonical specific heats, and the bimodality of the energy distribution function at the transition temperatures. Models for a good folder are shown to be quite robust against perturbations in the interaction potential parameters.Comment: 4 pages, 4 figure

Dry and wet interfaces: Influence of solvent particles on molecular recognition

We present a coarse-grained lattice model to study the influence of water on the recognition process of two rigid proteins. The basic model is formulated in terms of the hydrophobic effect. We then investigate several modifications of our basic model showing that the selectivity of the recognition process can be enhanced by considering the explicit influence of single solvent particles. When the number of cavities at the interface of a protein-protein complex is fixed as an intrinsic geometric constraint, there typically exists a characteristic fraction that should be filled with water molecules such that the selectivity exhibits a maximum. In addition the optimum fraction depends on the hydrophobicity of the interface so that one has to distinguish between dry and wet interfaces.Comment: 11 pages, 7 figure

Evolution of the potential-energy surface of amorphous silicon

The link between the energy surface of bulk systems and their dynamical properties is generally difficult to establish. Using the activation-relaxation technique (ART nouveau), we follow the change in the barrier distribution of a model of amorphous silicon as a function of the degree of relaxation. We find that while the barrier-height distribution, calculated from the initial minimum, is a unique function that depends only on the level of distribution, the reverse-barrier height distribution, calculated from the final state, is independent of the relaxation, following a different function. Moreover, the resulting gained or released energy distribution is a simple convolution of these two distributions indicating that the activation and relaxation parts of a the elementary relaxation mechanism are completely independent. This characterized energy landscape can be used to explain nano-calorimetry measurements.Comment: 5 pages, 4 figure

Design of Copolymeric Materials

We devise a method for designing materials that will have some desired structural characteristics. We apply it to multiblock copolymers that have two different types of monomers, A and B. We show how to determine what sequence of A's and B's should be synthesised in order to give a particular structure and morphology. %For example in a melt of such %polymers, one may wish to engineer a body-centered %cubic structure. Using this method in conjunction with the theory of microphase separation developed by Leibler, we show it is possible to efficiently search for a desired morphology. The method is quite general and can be extended to design isolated heteropolymers, such as proteins, with desired structural characteristics. We show that by making certain approximations to the exact algorithm, a method recently proposed by Shakhnovich and Gutin is obtained. The problems with this method are discussed and we propose an improved approximate algorithm that is computationally efficient.Comment: 15 pages latex 2.09 and psfig, 1 postscript figure