Free-energy calculations for semi-flexible macromolecules: Applications to DNA knotting and looping

Giovan, Stefan M.; Scharein, Robert G.; Hanke, Andreas; Levene, Stephen D.

doi:10.1063/1.4900657

Cited by 8 publications

(21 citation statements)

References 93 publications

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“…. In the Partition Function and Free Energy for a Circular Chain section, we discuss the numerical computation of the partition function

Q_{c i r}

for a circular chain using the TI‐NMA method and obtain the corresponding NMA result

Q_{c i r}^{(N M A)}

. In the Comparison of J‐Factor Values Obtained by NMA and TI‐NMA section, we obtain the J factor,

J

, as a universal function of

L / P

and compare the exact result for

J

with the corresponding NMA result,

J_{N M A}

.…”

Section: Theory and Resultsmentioning

confidence: 99%

“…where the elastic constants

c_{b}

c_{s}

are the same as in the Partition Function for a Linear Chain section. We compute the partition function

Q_{c i r}

and the free energy

F_{c i r} = - k_{B} T \ln true(Q_{c i r} true)

using the TI‐NMA method presented in reference and summarized for the present case in Figure . In this method, a circular molecular state,

C

, is gradually transformed into a harmonically constrained reference state

C_{0}

, which corresponds to the minimum energy conformation.…”

Section: Theory and Resultsmentioning

confidence: 99%

“…Following the procedure outlined in Ref. , we obtain

Q_{c i r}^{(N M A)} true(N true) = \exp true(- β E_{0} true) \frac{V}{a^{3}} {true(\frac{b_{0}^{3}}{a^{3}} true)}^{N - 1} N^{3 / 2} 8 π^{2} \sqrt{I_{x} I_{y} I_{z}} {\prod_{m = 7}^{3 N} true(\frac{2 π}{ν_{m}} true)}^{1 / 2}

where

E_{0} = k_{B} T c_{b} N true[1 - \cos true(2 π / N true) true]

is the energy of the minimum conformation

{\overset{⇀}{r}}_{0}

and

I_{x}

I_{y}

I_{z}

are the principal moments of inertia of

{\overset{⇀}{r}}_{0}

in units of

b_{0}

(we here assume that each vertex of the chain is associated with a unit mass). The unitless quantities

v_{m}

in Eq.…”

Section: Theory and Resultsmentioning

confidence: 99%

“…The objective of the present study is to test the validity of HA for the cyclization probability or J factor of a simple homogeneous wormlike chain without torsional elastic energy. To this end, we compare values of the J factor computed by the method of normal‐mode analysis (NMA), which is rigorously equivalent to HA computations, with the corresponding exact result for the J factor computed by a new method that combines NMA with thermodynamic integration, a technique we denote TI‐NMA . This allows us to characterize the validity of HA (and NMA) in terms of a universal, model‐independent function, which depends only on the ratio

L / P

, where

L

is the contour length and

P

is the persistence length of the semi‐flexible chain.…”

Section: Introductionmentioning

confidence: 99%

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DNA cyclization and looping in the wormlike limit: Normal modes and the validity of the harmonic approximation

2015

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For much of the last three decades Monte Carlo-simulation methods have been the standard approach for accurately calculating the cyclization probability, J, or J factor, for DNA models having sequencedependent bends or inhomogeneous bending flexibility. Within the last ten years, however, approaches based on harmonic analysis of semi-flexible polymer models have been introduced, which offer much greater computational efficiency than Monte Carlo techniques. These methods consider the ensemble of molecular conformations in terms of harmonic fluctuations about a well-defined elastic-energy minimum.However, the harmonic approximation is only applicable for small systems, because the accessible conformation space of larger systems is increasingly dominated by anharmonic contributions. In the case of computed values of the J factor, deviations of the harmonic approximation from the exact value of J as a function of DNA length have not been characterized. Using a recent, numerically exact method that accounts for both anharmonic and harmonic contributions to J for wormlike chains of arbitrary size, we report here the apparent error that results from neglecting anharmonic behavior. For wormlike chains having contour lengths less than four times the persistence length the error in J arising from the harmonic approximation is generally small, amounting to free energies less than the thermal energy, k B T. For larger systems, however, the deviations between harmonic and exact J values increase approximately linearly with size.

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“…. In the Partition Function and Free Energy for a Circular Chain section, we discuss the numerical computation of the partition function

Q_{c i r}

for a circular chain using the TI‐NMA method and obtain the corresponding NMA result

Q_{c i r}^{(N M A)}

. In the Comparison of J‐Factor Values Obtained by NMA and TI‐NMA section, we obtain the J factor,

J

, as a universal function of

L / P

and compare the exact result for

J

with the corresponding NMA result,

J_{N M A}

.…”

Section: Theory and Resultsmentioning

confidence: 99%

“…where the elastic constants

c_{b}

c_{s}

are the same as in the Partition Function for a Linear Chain section. We compute the partition function

Q_{c i r}

and the free energy

F_{c i r} = - k_{B} T \ln true(Q_{c i r} true)

using the TI‐NMA method presented in reference and summarized for the present case in Figure . In this method, a circular molecular state,

C

, is gradually transformed into a harmonically constrained reference state

C_{0}

, which corresponds to the minimum energy conformation.…”

Section: Theory and Resultsmentioning

confidence: 99%

“…Following the procedure outlined in Ref. , we obtain

Q_{c i r}^{(N M A)} true(N true) = \exp true(- β E_{0} true) \frac{V}{a^{3}} {true(\frac{b_{0}^{3}}{a^{3}} true)}^{N - 1} N^{3 / 2} 8 π^{2} \sqrt{I_{x} I_{y} I_{z}} {\prod_{m = 7}^{3 N} true(\frac{2 π}{ν_{m}} true)}^{1 / 2}

where

E_{0} = k_{B} T c_{b} N true[1 - \cos true(2 π / N true) true]

is the energy of the minimum conformation

{\overset{⇀}{r}}_{0}

and

I_{x}

I_{y}

I_{z}

are the principal moments of inertia of

{\overset{⇀}{r}}_{0}

in units of

b_{0}

(we here assume that each vertex of the chain is associated with a unit mass). The unitless quantities

v_{m}

in Eq.…”

Section: Theory and Resultsmentioning

confidence: 99%

L / P

, where

L

is the contour length and

P

is the persistence length of the semi‐flexible chain.…”

Section: Introductionmentioning

confidence: 99%

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DNA cyclization and looping in the wormlike limit: Normal modes and the validity of the harmonic approximation

2015

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“…Consequently, switching the counterion environment can change the twist/writhe partition in supercoiled DNA. Electron microscopy, atomic force microscopy (AFM) (Bednar et al 1994; Bussiek et al 2003; Cherny and Jovin 2001; Shlyakhtenko et al 2003) and computer modelling at the both the polymer (Giovan et al 2014; Schlick et al 1994; Zheng and Vologodskii 2009) and atomistic level (but within a continuum solvent approximation) (Mitchell and Harris 2013) has shown that positively charged counterions promote the compaction of supercoiled DNA into complex topologies in supercoiled plasmids.…”

Section: Dna Counterions and Topologymentioning

confidence: 99%

Protein/DNA interactions in complex DNA topologies: expect the unexpected

2016

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DNA supercoiling results in compacted DNA structures that can bring distal sites into close proximity. It also changes the local structure of the DNA, which can in turn influence the way it is recognised by drugs, other nucleic acids and proteins. Here, we discuss how DNA supercoiling and the formation of complex DNA topologies can affect the thermodynamics of DNA recognition. We then speculate on the implications for transcriptional control and the three-dimensional organisation of the genetic material, using examples from our own simulations and from the literature. We introduce and discuss the concept of coupling between the multiple length-scales associated with hierarchical nuclear structural organisation through DNA supercoiling and topology.

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