Modelling DNA loops using continuum and statistical mechanics One contribution of 16 to a Theme ‘The mechanics of DNA’

Balaeff, Alexander; Koudella, C. R.; Mahadevan, L.; Schulten, Klaus

doi:10.1098/rsta.2004.1384

Cited by 34 publications

(19 citation statements)

References 36 publications

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“…The viscous damping coefficient corresponding to a rod of radius r D and length B moving sideways through water is B ζ, with ζ given by Eq. (14). Putting this together, our back-of-the-envelope estimate for the prefactor is [see Eq.…”

Section: B Order Of Magnitude Estimates Of the Dynamical Prefactormentioning

confidence: 99%

“…The simplest diffusion tensor produces motion proportional to the local forces, making it diagonal in segment number n and coordinate i: The viscous diffusion constants are set so they reproduce the known diffusion constant for a straight cylinder of length B/kT (the bending persistence length) and radius r D = 1.2 nm: [14,15] …”

Section: B Transition State Theory: the Basic Ideamentioning

confidence: 99%

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Nucleation at the DNA supercoiling transition

Daniels

Sethna

2011

Phys. Rev. E

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Twisting DNA under a constant applied force reveals a thermally activated transition into a state with a supercoiled structure known as a plectoneme. Using transition state theory, we predict the rate of this plectoneme nucleation to be of order 10 4 Hz. We reconcile this with experiments that have measured hopping rates of order 10 Hz by noting that the viscous drag on the bead used to manipulate the DNA limits the measured rate. We find that the intrinsic bending caused by disorder in the base-pair sequence is important for understanding the free energy barrier that governs the transition. Both analytic and numerical methods are used in the calculations. We provide extensive details on the numerical methods for simulating the elastic rod model with and without disorder.

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Section: B Order Of Magnitude Estimates Of the Dynamical Prefactormentioning

confidence: 99%

Section: B Transition State Theory: the Basic Ideamentioning

confidence: 99%

Nucleation at the DNA supercoiling transition

Daniels

Sethna

2011

Phys. Rev. E

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“…Here, s is the arclength that parameterizes the elastic loop, L ϭ 258.4 Å is the length of the loop, ␤ 1 ϭ 0.8 ϫ 10 Ϫ19 erg⅐cm (1 erg ϭ 0.1 J), ␤ 2 ϭ 3.2 ϫ 10 Ϫ19 erg⅐cm, and ␥ ϭ 3 ϫ 10 Ϫ19 erg⅐cm are the elastic moduli of DNA bending and twisting (15,25,26), K 1 , K 2 , and ⍀ are the local curvatures and twist, respectively, and ⍀ o ϭ 34.6°per bp is the intrinsic twist of DNA (10,15,24). Electrostatic interaction terms, negligible for this loop at the chosen ionic strength of 100 mM, were excluded from the computations (10).…”

Section: Dna Loop Modelmentioning

confidence: 99%

“…1c). The equilibrium structure of the ribbon was obtained by solving the system of Kirchhoff equations of elasticity, which assume balance of the elastic stress at every cross-section along the loop, thereby minimizing the energy functional (10,15,24),…”

Section: Dna Loop Modelmentioning

confidence: 99%

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Structural dynamics of the lac repressor–DNA complex revealed by a multiscale simulation

Villa

Balaeff

Schulten

2005

Proc. Natl. Acad. Sci. U.S.A.

134

157

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A multiscale simulation of a complex between the lac repressor protein (LacI) and a 107-bp-long DNA segment is reported. The complex between the repressor and two operator DNA segments is described by all-atom molecular dynamics; the size of the simulated system comprises either 226,000 or 314,000 atoms. The DNA loop connecting the operators is modeled as a continuous elastic ribbon, described mathematically by the nonlinear Kirchhoff differential equations with boundary conditions obtained from the coordinates of the terminal base pairs of each operator. The forces stemming from the looped DNA are included in the molecular dynamics simulations; the loop structure and the forces are continuously recomputed because the protein motions during the simulations shift the operators and the presumed termini of the loop. The simulations reveal the structural dynamics of the LacI-DNA complex in unprecedented detail. The multiple domains of LacI exhibit remarkable structural stability during the simulation, moving much like rigid bodies. LacI is shown to absorb the strain from the looped DNA mainly through its mobile DNA-binding head groups. Even with large fluctuating forces applied, the head groups tilt strongly and keep their grip on the operator DNA, while the remainder of the protein retains its V-shaped structure. A simulated opening of the cleft of LacI by 500-pN forces revealed the interactions responsible for locking LacI in the V-conformation.protein-DNA interaction ͉ molecular dynamics ͉ elastic rod model ͉ DNA loop ͉ large-scale protein motion T he lac repressor (LacI) is a celebrated DNA-binding protein that regulates the function of the lac operon (1), a set of genes responsible for the lactose metabolism in Escherichia coli. In the absence of lactose, LacI inhibits the expression of the operon by binding to two of three specifically recognized DNA sites, called operators, and causing the DNA between the operators to fold into a loop (2-4). Depending on which operators are bound, the loop may have a length of either 384 or 75 bp (4, 5). The smaller loop contains the promoter of the lac operon, which includes binding sites for RNA polymerase and the activator protein CAP (1).Several x-ray structures of LacI, both alone and in complex with DNA, were reported (4, 6, 7). The repressor is a homotetramer folded into a dimer of dimers, two massive ''arms'' connected at the ends by means of a four-helix bundle (Fig. 1). Each arm consists of a core and a DNA-binding head group domain; the lactose binding sites divide the core domains into two subdomains. This architecture is essential for the function of LacI. The protein binds two operators with its two head groups and holds them close together, enforcing the interoperator loop, while leaving the lactose binding sites inside the core domains open for lactose molecules to enter, disrupt the repressor, and induce the expression of the lac operon. At the same time, the loose connections between the LacI domains imply a great degree of structural flexibility that LacI n...

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Large‐amplitude fast motions in double‐stranded DNA driven by solvent thermal fluctuations

Shih

Georghiou

2006

Biopolymers

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The nature of the internal dynamics of double-stranded DNA in aqueous environment remains to be established. We consider the motions to stem from thermal fluctuations/dissipations of the harmonic modes of beads (bases and sugars) in a cylindrical geometry that are tracked through the stochastic Langevin trajectories; these are characterized by parameters obtained from published data. The present approach has allowed a comparative study of the dynamics for DNA lengths in the range of 20-600 base pairs. For this range, we find that rotational motions about directions parallel to the helix axis (opening, twist) and perpendicular to it (propeller-twist, roll) contribute significantly to the dynamics. For a 20-mer at a solvent viscosity of 1 cP, the calculated fluorescence anisotropy profile exhibits a fast decay in the subnanosecond range due to large-amplitude fluctuations at the mesoscopic level. This feature reproduces the experimental behavior well, and suggests a possible way for the initiation of biological processes: they may be suddenly triggered on this scale through the occurrence of favorable thermal fluctuations. This analysis also reveals that, as is the case for a 20-mer, the dynamics of longer N-mers are dominated by internal motions, and are modulated by the viscosity of the solvent, in agreement with our previous experimental observations. Moreover, the model indicates that occurrence of partially concerted rotations of the bases due to thermal fluctuations can possibly be sustained over a DNA length of the order of 100 A at 1 ns, suggesting a possible mechanism for action-at-a-distance in transcription.

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Modelling DNA loops using continuum and statistical mechanics One contribution of 16 to a Theme ‘The mechanics of DNA’

Cited by 34 publications

References 36 publications

Nucleation at the DNA supercoiling transition

Nucleation at the DNA supercoiling transition

Structural dynamics of the lac repressor–DNA complex revealed by a multiscale simulation

Large‐amplitude fast motions in double‐stranded DNA driven by solvent thermal fluctuations

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