Dynamics of Small Loops in DNA Molecules
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.
133
- 10.1080/07391102.1985.10507616
- Feb 1, 1985
- Journal of Biomolecular Structure and Dynamics
98
- 10.1006/jmbi.1998.2170
- Nov 1, 1998
- Journal of Molecular Biology
105
- 10.1063/1.455790
- Apr 1, 1989
- The Journal of Chemical Physics
83
- 10.1016/0959-440x(92)90227-x
- Jun 1, 1992
- Current Opinion in Structural Biology
142
- 10.1016/0022-2836(91)90745-r
- Feb 1, 1991
- Journal of Molecular Biology
34543
- 10.1063/1.1699114
- Jun 1, 1953
- The Journal of Chemical Physics
43
- 10.1021/ma00028a041
- Jan 1, 1992
- Macromolecules
340
- 10.1016/0022-2836(92)90533-p
- Oct 1, 1992
- Journal of Molecular Biology
118
- 10.1016/0022-2836(86)90381-5
- May 1, 1986
- Journal of Molecular Biology
105
- 10.1021/ma00098a016
- Sep 1, 1994
- Macromolecules
- Research Article
10
- 10.1063/1.1461359
- Apr 2, 2002
- The Journal of Chemical Physics
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.
- Research Article
5
- 10.1103/physreve.96.022501
- Aug 7, 2017
- Physical review. E
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.
- Research Article
17
- 10.1063/1.4802258
- May 6, 2013
- The Journal of Chemical Physics
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.
- Research Article
18
- 10.1016/j.bpj.2008.11.013
- Feb 1, 2009
- Biophysical Journal
Theoretical Analysis of Disruptions in DNA Minicircles
- Research Article
30
- 10.1103/physreve.72.061902
- Dec 2, 2005
- Physical Review E
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.
- Research Article
17
- 10.1063/1.4929994
- Sep 10, 2015
- The Journal of Chemical Physics
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.
- Research Article
25
- 10.1093/nar/gkn051
- Feb 14, 2008
- Nucleic Acids Research
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.
- Research Article
5
- 10.1063/1.2430712
- Jan 28, 2007
- The Journal of Chemical Physics
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.
- Book Chapter
- 10.1201/b17282-10
- Aug 21, 2014
Minimal Models for the Structure and Dynamics of Nucleic Acids
- Book Chapter
1
- 10.1017/cbo9781139542371.004
- Feb 28, 2015
Equilibrium large-scale conformational properties of DNA
- Peer Review Report
- 10.7554/elife.01775.016
- Nov 22, 2013
Decision letter: Single-molecule tracking of the transcription cycle by sub-second RNA detection
- Abstract
- 10.1016/j.bpj.2013.11.1616
- Jan 1, 2014
- Biophysical Journal
Single Molecule Studies of Sequence Dependence Elasticity in DNA
- Supplementary Content
29
- 10.1002/1522-2683(200109)22:16<3357::aid-elps3357>3.0.co;2-c
- Sep 1, 2001
- ELECTROPHORESIS
By means of atomic force microscopy (AFM), we performed the direct imaging of DNA molecules (200, 500, 1000 bp) in a Tris-borate buffer solution, and measured the contour length and the end-to-end distance of DNA. Processing the data according to the worm-like chain model, we calculated the persistence length of the double-stranded DNA. Based on the analysis of the contour length and the persistence length, we discussed the interactions between DNA and an intercalating fluorescence dye (YO-PRO-1). YO-PRO-1 stacks between the base pairs and extends the contour length of DNA, changing the electric charge and the persistence length of DNA. From AFM measurement, we investigated directly the relationship between the persistence length and the number of the YO-PRO-1 intercalating to DNA. We will discuss on the relationship between the effect of an intercalating dye on the electrophoretic behavior and the conformational changes of DNA with an intercalating dye.
- Research Article
32
- 10.1016/j.molcel.2008.12.023
- Jan 1, 2009
- Molecular cell
Second-End Capture in DNA Double-Strand Break Repair Promoted by Brh2 Protein of Ustilago maydis
- Research Article
- 10.1016/j.bpj.2016.04.016
- May 1, 2016
- Biophysical Journal
When Computer Simulation Excels Experiment
- Research Article
16
- 10.1063/1.4979605
- Mar 1, 2017
- Biomicrofluidics
Genome mapping involves the confinement of long DNA molecules, in excess of 150 kilobase pairs, in nanochannels near the circa 50 nm persistence length of DNA. The fidelity of the map relies on the assumption that the DNA is linearized by channel confinement, which assumes the absence of knots. We have computed the probability of forming different knot types and the size of these knots for long chains (approximately 164 kilobase pairs) via pruned-enriched Rosenbluth method simulations of a discrete wormlike chain model of DNA in channel sizes ranging from 35 nm to 60 nm. Compared to prior simulations of short DNA in similar confinement, these long molecules exhibit both complex knots, with up to seven crossings, and multiple knots per chain. The knotting probability is a very strong function of channel size, ranging from 0.3% to 60%, and rationalized in the context of Odijk's theory for confined semiflexible chains. Overall, the knotting probability and knot size obtained from these equilibrium measurements are not consistent with experimental measurements of the properties of anomalously bright regions along the DNA backbone during genome mapping experiments. This result suggests that these events in experiments are either knots formed during the processing of the DNA prior to injection into the nanochannel or regions of locally high DNA concentration without a topological constraint. If so, knots during genome mapping are not an intrinsic problem for genome mapping technology.
- Research Article
61
- 10.1371/journal.pone.0000136
- Dec 27, 2006
- PLoS ONE
Interactions of E. coli lac repressor (LacR) with a pair of operator sites on the same DNA molecule can lead to the formation of looped nucleoprotein complexes both in vitro and in vivo. As a major paradigm for loop-mediated gene regulation, parameters such as operator affinity and spacing, repressor concentration, and DNA bending induced by specific or non-specific DNA-binding proteins (e.g., HU), have been examined extensively. However, a complete and rigorous model that integrates all of these aspects in a systematic and quantitative treatment of experimental data has not been available. Applying our recent statistical-mechanical theory for DNA looping, we calculated repression as a function of operator spacing (58–156 bp) from first principles and obtained excellent agreement with independent sets of in-vivo data. The results suggest that a linear extended, as opposed to a closed v-shaped, LacR conformation is the dominant form of the tetramer in vivo. Moreover, loop-mediated repression in wild-type E. coli strains is facilitated by decreased DNA rigidity and high levels of flexibility in the LacR tetramer. In contrast, repression data for strains lacking HU gave a near-normal value of the DNA persistence length. These findings underscore the importance of both protein conformation and elasticity in the formation of small DNA loops widely observed in vivo, and demonstrate the utility of quantitatively analyzing gene regulation based on the mechanics of nucleoprotein complexes.
- Research Article
6
- 10.1074/jbc.m603977200
- Sep 1, 2006
- Journal of Biological Chemistry
Type II topoisomerases change DNA topology by passage of one DNA duplex (the transfer, T-segment) through a transient double-stranded break in another (the gate, G-segment). Here we monitor the passage between short double-stranded DNA segments within long single-stranded DNA circles that leads to catenation of the circles. To facilitate catenation, the circles were brought into close proximity using a tethering oligonucleotide, which was removed after the reaction was complete. We varied the length and the composition of the reacting DNA segments. The minimal DNA duplex length at which we detected catenation was 50-60 bp for DNA gyrase and 40 bp for topoisomerase IV (Topo IV). For Topo IV, catenation was observed when one, but not both, of the DNA-DNA duplexes was replaced by a DNA-RNA duplex. Topo IV cleaved the DNA-DNA duplex, but not the DNA-RNA duplex implying that the DNA-RNA duplex can be a T-segment but not a G-segment.
- Research Article
51
- 10.1002/anie.201100371
- May 6, 2011
- Angewandte Chemie International Edition
Fluorescence nanoscopy of single DNA molecules by using stimulated emission depletion (STED).
- Research Article
46
- 10.1038/emboj.2011.180
- Jun 10, 2011
- The EMBO Journal
In spite of extensive research, the mechanism by which MutS initiates DNA mismatch repair (MMR) remains controversial. We use atomic force microscopy (AFM) to capture how MutS orchestrates the first step of E. coli MMR. AFM images captured two types of MutS/DNA complexes: single-site binding and loop binding. In most of the DNA loops imaged, two closely associated MutS dimers formed a tetrameric complex in which one of the MutS dimers was located at or near the mismatch. Surprisingly, in the presence of ATP, one MutS dimer remained at or near the mismatch site and the other, while maintaining contact with the first dimer, relocated on the DNA by reeling in DNA, thereby producing expanding DNA loops. Our results indicate that MutS tetramers composed of two non-equivalent MutS dimers drive E. coli MMR, and these new observations now reconcile the apparent contradictions of previous 'sliding' and 'bending/looping' models of interaction between mismatch and strand signal.
- Research Article
93
- 10.1371/journal.pone.0005621
- May 25, 2009
- PLoS ONE
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.
- Research Article
98
- 10.1006/jmbi.1998.2170
- Nov 1, 1998
- Journal of Molecular Biology
Internal motion of supercoiled DNA: brownian dynamics simulations of site juxtaposition
- Research Article
38
- 10.1016/j.molcel.2009.05.020
- Jun 1, 2009
- Molecular cell
Mechanical Constraints on Hin Subunit Rotation Imposed by the Fis/Enhancer System and DNA Supercoiling during Site-Specific Recombination
- Research Article
16
- 10.1063/1.3682984
- Mar 1, 2012
- The Journal of Chemical Physics
We have performed canonical ensemble Monte Carlo simulations of a primitive DNA model to study the conformation of 2.56 ~ 21.8 μm long DNA molecules confined in nanochannels at various ionic concentrations with the comparison of our previous experimental findings. In the model, the DNA molecule is represented as a chain of charged hard spheres connected by fixed bond length and the nanochannels as planar hard walls. System potentials consist of explicit electrostatic potential along with short-ranged hard-sphere and angle potentials. Our primitive model system provides valuable insight into the DNA conformation, which cannot be easily obtained from experiments or theories. First, the visualization and statistical analysis of DNA molecules in various channel dimensions and ionic strengths verified the formation of locally coiled structures such as backfolding or hairpin and their significance even in highly stretched states. Although the folding events mostly occur within the region of ~0.5 μm from both chain ends, significant portion of the events still take place in the middle region. Second, our study also showed that two controlling factors such as channel dimension and ionic strength widely used in stretching DNA molecules have different influence on the local DNA structure. Ionic strength changes local correlation between neighboring monomers by controlling the strength of electrostatic interaction (and thus the persistence length of DNA), which leads to more coiled local conformation. On the other hand, channel dimension controls the overall stretch by applying the geometric constraint to the non-local DNA conformation instead of directly affecting local correlation. Third, the molecular weight dependence of DNA stretch was observed especially in low stretch regime, which is mainly due to the fact that low stretch modes observed in short DNA molecules are not readily accessible to much longer DNA molecules, resulting in the increase in the stretch of longer DNA molecules.
- Research Article
33
- 10.1016/s0969-806x(03)00066-5
- Apr 22, 2003
- Radiation Physics and Chemistry
Free-radical-induced chain scission and cross-linking of polymers in aqueous solution—an overview
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