Synthesis 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-like" equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical 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 3-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.

Active biological processes like transcription, replication, recombination, DNA repair, and DNA packaging encounter bent DNA. Machineries associated with these processes interact with the DNA at short length (<100 base pair) scale. Thus, the study of elasticity of DNA at such length scale is very important. We use fully atomistic molecular dynamics (MD) simulations along with various theoretical methods to determine elastic properties of dsDNA of different lengths and base sequences. We also study DNA elasticity in nucleosome core particle (NCP) both in the presence and the absence of salt. We determine stretch modulus and persistence length of short dsDNA and nucleosomal DNA from contour length distribution and bend angle distribution, respectively. For short dsDNA, we find that stretch modulus increases with ionic strength while persistence length decreases. Calculated values of stretch modulus and persistence length for DNA are in quantitative agreement with available experimental data. The trend is opposite for NCP DNA. We find that the presence of histone core makes the DNA stiffer and thus making the persistence length 3-4 times higher than the bare DNA. Similarly, we also find an increase in the stretch modulus for the NCP DNA. Our study for the first time reports the elastic properties of DNA when it is wrapped around the histone core in NCP. We further show that the WLC model is inadequate to describe DNA elasticity at short length scale. Our results provide a deeper understanding of DNA mechanics and the methods are applicable to most protein-DNA complexes.

In eukaryotic cells, many motor proteins can move simultaneously on a single microtubule track. This leads to interesting collective phenomena like 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 a novel interaction parameter c, to account for an interesting mechano-chemical process which has not been considered in any earlier model. We have been able to extract all the parameters of the model, except c, from experimentally measured quantities. In contrast to earlier models of intra-cellular molecular motor traffic, our model assigns distinct "chemical" (or, conformational) states to each kinesin to account for the hydrolysis of 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 phaseseparated 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 mechano-chemical process captured by the parameter c.

Persistence length of double-stranded DNA (dsDNA) is known to decrease with an increase in ionic concentration of the solution. In contrast to this, here we show that the persistence length of dsDNA increases dramatically as a function of ionic liquid (IL) concentration. Using all atom explicit solvent molecular dynamics simulations and theoretical models, we present, for the first time, a systematic study to determine the mechanical properties of dsDNA in various hydrated ILs at different concentrations. We find that dsDNA in 50 wt % ILs have lower persistence length and stretch modulus in comparison to 80 wt % ILs. We further observe that both the persistence length and stretch modulus of dsDNA increase as we increase the concentration of ILs. The present trend of the stretch modulus and persistence length of dsDNA with IL concentration supports the predictions of the macroscopic elastic theory, in contrast to the behavior exhibited by dsDNA in monovalent salt. Our study further suggests the preferable ILs that can be used for maintaining DNA stability during long-term storage.