What do we know about DNA mechanics so far?

The DNA molecule, apart from carrying the genetic information, plays a crucial role in a variety of biological processes and finds applications in drug design, nanotechnology and nanoelectronics. The molecule undergoes significant structural transitions under the influence of forces due to physiological and non-physiological environments. Here, we summarize the insights gained from simulations and single-molecule experiments on the structural transitions and mechanics of DNA under force, as well as its elastic properties, in various environmental conditions, and discuss appealing future directions.

Ionic liquids make DNA rigid.

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.

Overstretching of B-DNA with various pulling protocols: Appearance of structural polymorphism and S-DNA.

We report a structural polymorphism of the S-DNA when a canonical B-DNA is stretched under different pulling protocols and provide a fundamental molecular understanding of the DNA stretching mechanism. Extensive all atom molecular dynamics simulations reveal a clear formation of S-DNA when the B-DNA is stretched along the 3' directions of the opposite strands (OS3) and is characterized by the changes in the number of H-bonds, entropy, and free energy. Stretching along the 5' directions of the opposite strands (OS5) leads to force induced melting form of the DNA. Interestingly, stretching along the opposite ends of the same strand leads to a coexistence of both the S- and melted M-DNA structures. We also do the structural characterization of the S-DNA by calculating various helical parameters. We find that the S-DNA has a twist of ∼10° which corresponds to a helical repeat length of ∼36 base pairs in close agreement with the previous experimental results. Moreover, we find that the free energy barrier between the canonical and overstretched states of DNA is higher for the same termini pulling protocol in comparison to all other protocols considered in this work. Overall, our observations not only reconcile with the available experimental results qualitatively but also enhance the understanding of different overstretched DNA structures.

DNA Elasticity from Short DNA to Nucleosomal DNA.

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.

Conformational dynamics through an intermediate.

The self-assembly of biological and synthetic nanostructures commonly proceeds via intermediate states. In living systems in particular, the intermediates have the capacity to tilt the balance between functional and potentially fatal behavior. This work develops a statistical mechanical treatment of conformational dynamics through an intermediate under a variable force. An analytical solution is derived for the key experimentally measurable quantity-the distribution of forces at which a conformational transition occurs. The solution reveals rich kinetics over a broad range of parameters and enables one to locate the intermediate and extract the activation barriers and rate constants.

Footprint traversal by adenosine-triphosphate-dependent chromatin remodeler motor.

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.

Stochastic kinetics of ribosomes: single motor properties and collective behavior.

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.

Fluctuations in protein synthesis from a single RNA template: stochastic kinetics of ribosomes.

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.

Traffic of single-headed motor proteins KIF1A: effects of lane changing.

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.

Two-state model for helicase translocation and unwinding of nucleic acids.

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.

Intracellular transport by single-headed kinesin KIF1A: effects of single-motor mechanochemistry and steric interactions.

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.