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DNA polymerase (DNAP) is a dual-purpose enzyme that plays two opposite roles in two different situations during DNA replication. It plays its a normal role as a polymerase catalyzing the elongation of a new DNA molecule by adding a monomer. However, it can switch to the role of an exonuclease and shorten the same DNA by cleavage of the last incorporated monomer from the nascent DNA. Just as misincorporated nucleotides can escape exonuclease causing a replication error, the correct nucleotide may get sacrificed unnecessarily by erroneous cleavage. The interplay of polymerase and exonuclease activities of a DNAP is explored here by developing a minimal stochastic kinetic model of DNA replication. Exact analytical expressions are derived for a few key statistical distributions; these characterize the temporal patterns in the mechanical stepping and the chemical (cleavage) reaction. The Michaelis-Menten-like analytical expression derived for the average rates of these two processes not only demonstrate the effects of their coupling, but are also utilized to measure the extent of replication error and erroneous cleavage.

Adenosine-triphosphate (ATP)-dependent chromatin remodeling enzymes (CREs) are biomolecular motors in eukaryotic cells. These are driven by a chemical fuel, namely, ATP. CREs actively participate in many cellular processes that require accessibility of specific segments of DNA which are packaged as chromatin. The basic unit of chromatin is a nucleosome where 146 bp ∼ 50 nm of a double-stranded DNA (dsDNA) is wrapped around a spool formed by histone proteins. The helical path of histone-DNA contact on a nucleosome is also called "footprint." We investigate the mechanism of footprint traversal by a CRE that translocates along the dsDNA. Our two-state model of a CRE captures effectively two distinct chemical (or conformational) states in the mechanochemical cycle of each ATP-dependent CRE. We calculate the mean time of traversal. Our predictions on the ATP dependence of the mean traversal time can be tested by carrying out in vitro experiments on mononucleosomes.

Ribosome is a molecular machine that moves on a messenger RNA (mRNA) track while, simultaneously, polymerizing a protein using the mRNA also as the corresponding template. We define, and analytically calculate, two different measures of the efficiency of this machine. However, we argue that its performance is evaluated better in terms of the translational fidelity and the speed with which it polymerizes a protein. We define both these quantities and calculate these analytically. Fidelity is a measure of the quality of the products, while the total quantity of products synthesized in a given interval depends on the speed of polymerization. We show that for synthesizing a large quantity of proteins, it is not necessary to sacrifice the quality. We also explore the effects of the quality control mechanism on the strength of mechanochemical coupling. We suggest experiments for testing some of the ideas presented here.

Syntheses of protein molecules in a cell are carried out by ribosomes. A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an exact analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a "Michaelis-Menten-type" equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechanochemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes simultaneously move on the same mRNA track, while each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in three-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.

Proteins are polymerized by cyclic machines called ribosomes, which use their messenger RNA (mRNA) track also as the corresponding template, and the process is called translation. We explore, in depth and detail, the stochastic nature of the translation. We compute various distributions associated with the translation process; one of them--namely, the dwell time distribution--has been measured in recent single-ribosome experiments. The form of the distribution, which fits best with our simulation data, is consistent with that extracted from the experimental data. For our computations, we use a model that captures both the mechanochemistry of each individual ribosome and their steric interactions. We also demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise in translation. Finally, inspired by recent advances in the experimental techniques of manipulating single ribosomes, we make theoretical predictions on the force-velocity relation for individual ribosomes. In principle, all our predictions can be tested by carrying out in vitro experiments.

Helicases are molecular motors that unwind double-stranded nucleic acids (dsNA), such as DNA and RNA. Typically a helicase translocates along one of the NA single strands while unwinding and uses adenosine triphosphate (ATP) hydrolysis as an energy source. Here we model a helicase motor that can switch between two states, which could represent two different points in the ATP hydrolysis cycle. Our model is an extension of the earlier Betterton-Jülicher model of helicases to incorporate switching between two states. The main predictions of the model are the speed of unwinding of the dsNA and fluctuations around the average unwinding velocity. Motivated by a recent claim that the NS3 helicase of Hepatitis C virus follows a flashing-ratchet mechanism, we have compared the experimental results for the NS3 helicase with a special limit of our model which corresponds to the flashing-ratchet scenario. Our model accounts for one key feature of the experimental data on NS3 helicase. However, contradictory observations in experiments carried out under different conditions limit the ability to compare the model to experiments.

KIF1A kinesins are single-headed motor proteins which move on cylindrical nanotubes called microtubules (MTs). A normal MT consists of 13 protofilaments on which the equispaced motor binding sites form a periodic array. The collective movement of the kinesins on a MT is, therefore, analogous to vehicular traffic on multilane highways where each protofilament is the analog of a single lane. Does lane changing increase or decrease the motor flux per lane? We address this fundamental question here by appropriately extending a recent model [P. Greulich, Phys. Rev. E 75, 041905 (2007)]. By carrying out analytical calculations and computer simulations of this extended model, we predict that the flux per lane can increase or decrease with the increasing rate of lane changing, depending on the concentrations of motors and the rate of hydrolysis of ATP, the "fuel" molecules. Our predictions can be tested, in principle, by carrying out in vitro experiments with fluorescently labeled KIF1A molecules.

RNA polymerase (RNAP) is an enzyme that synthesizes a messenger RNA (mRNA) strand which is complementary to a single-stranded DNA template. From the perspective of physicists, an RNAP is a molecular motor that utilizes chemical energy input to move along the track formed by DNA. In many circumstances, which are described in this paper, a large number of RNAPs move simultaneously along the same track; we refer to such collective movements of the RNAPs as RNAP traffic. Here we develop a theoretical model for RNAP traffic by incorporating the steric interactions between RNAPs as well as the mechanochemical cycle of individual RNAPs during the elongation of the mRNA. By a combination of analytical and numerical techniques, we calculate the rates of mRNA synthesis and the average density profile of the RNAPs on the DNA track. We also introduce, and compute, two different measures of fluctuations in the synthesis of RNA. Analyzing these fluctuations, we show how the level of intrinsic noise in mRNA synthesis depends on the concentrations of the RNAPs as well as on those of some of the reactants and the products of the enzymatic reactions catalyzed by RNAP. We suggest appropriate experimental systems and techniques for testing our theoretical predictions.

In eukaryotic cells, many motor proteins can move simultaneously on a single microtubule track. This leads to interesting collective phenomena such as jamming. Recently we reported [Phys. Rev. Lett. 95, 118101 (2005)] a lattice-gas model which describes traffic of unconventional (single-headed) kinesins KIF1A. Here we generalize this model, introducing an interaction parameter c, to account for an interesting mechanochemical process. We have been able to extract all the parameters of the model, except c, from experimentally measured quantities. In contrast to earlier models of intracellular molecular motor traffic, our model assigns distinct "chemical" (or, conformational) states to each kinesin to account for the hydrolysis of adenosine triphosphate (ATP), the chemical fuel of the motor. Our model makes experimentally testable theoretical predictions. We determine the phase diagram of the model in planes spanned by experimentally controllable parameters, namely, the concentrations of kinesins and ATP. Furthermore, the phase-separated regime is studied in some detail using analytical methods and simulations to determine, e.g., the position of shocks. Comparison of our theoretical predictions with experimental results is expected to elucidate the nature of the mechanochemical process captured by the parameter c.

Many ribosomes simultaneously move on the same messenger RNA (mRNA), each synthesizing separately a copy of the same protein. In contrast to the earlier models, here we develop a "unified" theoretical model that not only incorporates the mutual exclusions of the interacting ribosomes, but also describes explicitly the mechanochemistry of each of these macromolecular machines during protein synthesis. Using analytical and numerical techniques of nonequilibrium statistical mechanics, we analyze the rates of protein synthesis and the spatiotemporal organization of the ribosomes in this model. We also predict how these properties would change with the changes in the rates of the various chemomechanical processes in each ribosome. Finally, we illustrate the power of this model by making experimentally testable predictions on the rates of protein synthesis and the density profiles of the ribosomes on some mRNAs in E-coli.

Microtubules are stiff filamentary proteins that constitute an important component of the cytoskeleton of cells. These are known to exhibit a dynamic instability. A steadily growing microtubule can suddenly start depolymerizing very rapidly; this phenomenon is known as a "catastrophe." However, often a shrinking microtubule is "rescued" and starts polymerizing again. Here we develop a model for the polymerization-depolymerization dynamics of microtubules in the presence of catastrophe-suppressing drugs. Solving the dynamical equations in the steady state, we derive exact analytical expressions for the length distributions of the microtubules tipped with drug-bound tubulin subunits as well as those of the microtubules, in the growing and shrinking phases, tipped with drug-free pure tubulin subunits. We also examine the stability of the steady-state solutions.

We incorporate the generic hierarchical architecture of foodwebs into a "unified" model that describes both micro- and macroevolutions within a single theoretical framework. This model describes the microevolution in detail by accounting for the birth, ageing, and natural death of individual organisms as well as prey-predator interactions on a hierarchical dynamic food web. It also provides a natural description of random mutations and speciation (origination) of species as well as their extinctions. The distribution of lifetimes of species follows an approximate power law only over a limited regime.

A recently proposed stochastic cellular automaton model [J. Phys. A 35, L573 (2002)], motivated by the motions of ants in a trail, is investigated in detail in this paper. The flux of ants in this model is sensitive to the probability of evaporation of pheromone, and the average speed of the ants varies nonmonotonically with their density. This remarkable property is analyzed here using phenomenological and microscopic approximations thereby elucidating the nature of the spatiotemporal organization of the ants. We find that the observations can be understood by the formation of loose clusters, i.e., space regions of enhanced, but not maximal, density.

We develop n-cluster mean-field theories (1 < or = n < or = 4) for calculating the flux and the gap distribution in the nonequilibrium steady states of the Katz-Lebowitz-Spohn model of the driven diffusive lattice gas, with attractive and repulsive interparticle interactions, in both one and two dimensions for arbitrary particle densities, temperature as well as the driving field. We compare our theoretical results with the corresponding numerical data we have obtained from the computer simulations to demonstrate the level of accuracy of our theoretical predictions. We also compare our results with those for some other prototype models, notably particle-hopping models of vehicular traffic, to demonstrate the qualitative features we have observed in the Katz-Lebowitz-Spohn model, emphasizing, in particular, the consequences of repulsive interparticle interactions.