Dynamics of Small Loops in DNA Molecules

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The kinetics and thermodynamics of loop formation by short segments of double-stranded DNA was studied by computer simulation. The DNA molecule was modeled as a discrete wormlike chain. Brownian dynamics was used to simulate the dynamic properties of the chain. Since the average time of loop formation, τa, grows sharply when the loop size drops below DNA persistence length, we were unable to simulate the process directly for such small loops. Instead, we used the relationship between the equilibrium probability of loop formation, P, τa, and the average time of loop decay, τd. The values of P and τd were simulated directly. A new Monte Carlo algorithm was developed allowing efficient calculation of P for small DNA loops. The algorithm is also applicable to more complex models of a polymer chain, particularly to DNA models with intrinsic curvature. We also considered loop formation by a segment of a DNA molecule and found that the values of τd and τa are weakly affected by the total chain size. Our results showed that the formation of small loops is a very slow process: for loops less than 50 nm in size τa can be comparable to the lifetime of the cell.

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CitationsShowing 10 of 42 papers
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Pivot-coupled grand canonical Monte Carlo method for ring simulations
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  • The Journal of Chemical Physics
  • James T Kindt

A new method is presented for the simulation of an ensemble of polymer rings of variable size at fixed monomer chemical potential. Called pivot-coupled grand canonical Monte Carlo (PC-GCMC), it is based on the directed addition or removal of a monomer to or from a ring, coupled to the pivot of a section of the ring to maintain the ring’s continuity. Application of PC-GCMC to single, isolated rings yields the free energy of the ring polymer as a function of number of monomers, information useful in determining equilibrium constants for polymer cyclization. Ring closure probabilities (“J-factors”) for flexible and semiflexible polymers, both ideal and self-avoiding, in two and three dimensions are obtained in close agreement with available results from theory and other simulation methods. New results are obtained for two-dimensional semiflexible polygons. Potential applications of the method to simulations of ring-forming equilibrium polymers, disklike micelles, and self-assembling polymer loops are discussed.

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Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius.
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Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.

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Kinetics of loop formation in worm-like chain polymers
  • May 6, 2013
  • The Journal of Chemical Physics
  • Reza Afra + 1 more

A common theoretical approach to calculating reaction kinetics is to approximate a high-dimensional conformational search with a one-dimensional diffusion along an effective reaction coordinate. We employed Brownian dynamics simulations to test the validity of this approximation for loop formation kinetics in the worm-like chain polymer model. This model is often used to describe polymers that exhibit backbone stiffness beyond the monomer length scale. We find that one-dimensional diffusion models overestimate the looping time and do not predict the quantitatively correct dependence of looping time on chain length or capture radius. Our findings highlight the difficulty of describing high-dimensional polymers with simple kinetic theories.

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Theoretical Analysis of Disruptions in DNA Minicircles
  • Feb 1, 2009
  • Biophysical Journal
  • Xiaozhong Zheng + 1 more

Theoretical Analysis of Disruptions in DNA Minicircles

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Protein-mediated DNA loops: Effects of protein bridge size and kinks
  • Dec 2, 2005
  • Physical Review E
  • Nicolas Douarche + 1 more

This paper focuses on the probability that a portion of DNA closes on itself through thermal fluctuations. We investigate the dependence of this probability upon the size of a protein bridge and/or the presence of a kink at half DNA length. The DNA is modeled by the wormlike chain model, and the probability of loop formation is calculated in two ways: exact numerical evaluation of the constrained path integral and the extension of the Shimada and Yamakawa saddle point approximation. For example, we find that the looping free energy of a 100-base-pairs DNA decreases from 24 kBT to 13 kBT when the loop is closed by a protein of r=10 length. It further decreases 5 kBT to when the loop has a kink of 120 degrees at half-length.

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  • 10.1063/1.4929994
Extreme bendability of DNA double helix due to bending asymmetry.
  • Sep 10, 2015
  • The Journal of Chemical Physics
  • H Salari + 3 more

Experimental data of the DNA cyclization (J-factor) at short length scales exceed the theoretical expectation based on the wormlike chain (WLC) model by several orders of magnitude. Here, we propose that asymmetric bending rigidity of the double helix in the groove direction can be responsible for extreme bendability of DNA at short length scales and it also facilitates DNA loop formation at these lengths. To account for the bending asymmetry, we consider the asymmetric elastic rod (AER) model which has been introduced and parametrized in an earlier study [B. Eslami-Mossallam and M. R. Ejtehadi, Phys. Rev. E 80, 011919 (2009)]. Exploiting a coarse grained representation of the DNA molecule at base pair (bp) level and using the Monte Carlo simulation method in combination with the umbrella sampling technique, we calculate the loop formation probability of DNA in the AER model. We show that the DNA molecule has a larger J-factor compared to the WLC model which is in excellent agreement with recent experimental data.

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Dynamics and consequences of DNA looping by the FokI restriction endonuclease
  • Feb 14, 2008
  • Nucleic Acids Research
  • Lucy E Catto + 3 more

Genetic events often require proteins to be activated by interacting with two DNA sites, trapping the intervening DNA in a loop. While much is known about looping equilibria, only a few studies have examined DNA-looping dynamics experimentally. The restriction enzymes that cut DNA after interacting with two recognition sites, such as FokI, can be used to exemplify looping reactions. The reaction pathway for FokI on a supercoiled DNA with two sites was dissected by fast kinetics to reveal, in turn: the initial binding of a protein monomer to each site; the protein–protein association to form the dimer, trapping the loop; the subsequent phosphodiester hydrolysis step. The DNA motion that juxtaposes the sites ought on the basis of Brownian dynamics to take ∼2 ms, but loop capture by FokI took 230 ms. Hence, DNA looping by FokI is rate limited by protein association rather than DNA dynamics. The FokI endonuclease also illustrated activation by looping: it cut looped DNA 400 times faster than unlooped DNA.

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Statistical properties and kinetics of end-end contact formation of unfolded polypeptides: A systematic molecular dynamics study
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  • The Journal of Chemical Physics
  • Guanghui Ping + 2 more

The authors have systematically examined the statistical properties of the unfolded states of series of polypeptides and the kinetics of their end-to-end contact (ring closure) formation by molecular dynamics simulations. The formation of an end-to-end contact follows a single-exponential decay as measured by the first-passage time. It is shown that the shifted Gaussian chain model can be applied to describe the dimensions of glycine-rich polypeptides at high temperature. However, notable deviation from the ideal Gaussian chain model was observed at lower temperatures particularly for those polypeptides without glycines, due to the tendency to form local structures.

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Equilibrium large-scale conformational properties of DNA
  • Feb 28, 2015
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Concentration and Length Dependence of DNA Looping in Transcriptional Regulation
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  • PLoS ONE
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In many cases, transcriptional regulation involves the binding of transcription factors at sites on the DNA that are not immediately adjacent to the promoter of interest. This action at a distance is often mediated by the formation of DNA loops: Binding at two or more sites on the DNA results in the formation of a loop, which can bring the transcription factor into the immediate neighborhood of the relevant promoter. These processes are important in settings ranging from the historic bacterial examples (bacterial metabolism and the lytic-lysogeny decision in bacteriophage), to the modern concept of gene regulation to regulatory processes central to pattern formation during development of multicellular organisms. Though there have been a variety of insights into the combinatorial aspects of transcriptional control, the mechanism of DNA looping as an agent of combinatorial control in both prokaryotes and eukaryotes remains unclear. We use single-molecule techniques to dissect DNA looping in the lac operon. In particular, we measure the propensity for DNA looping by the Lac repressor as a function of the concentration of repressor protein and as a function of the distance between repressor binding sites. As with earlier single-molecule studies, we find (at least) two distinct looped states and demonstrate that the presence of these two states depends both upon the concentration of repressor protein and the distance between the two repressor binding sites. We find that loops form even at interoperator spacings considerably shorter than the DNA persistence length, without the intervention of any other proteins to prebend the DNA. The concentration measurements also permit us to use a simple statistical mechanical model of DNA loop formation to determine the free energy of DNA looping, or equivalently, the for looping.

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  • 10.1006/jmbi.1998.2170
Internal motion of supercoiled DNA: brownian dynamics simulations of site juxtaposition
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