Forces by and on a Polymer Grafted to a Repulsive Wall

Odenheimer, Jens; Heermann, Dieter W.; Brill, Michael

doi:10.1142/s0129183105008151

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…4, where we divided averaged square distances by N 2ν and plotted them against 1/ √ N . The ratio z 2 N / x 2 N + y 2 N increases with N as found also in [23], but it converges for N → ∞ to a finite value, 0.938 ± 0.002. In contrast to [23] we see no indication that either z 2 N or x 2 N + y 2 N scales with an exponent different from the bulk Flory exponent.…”

Section: Results: A-thermal Wallssupporting

confidence: 76%

Simulations of grafted polymers in a good solvent

Grassberger¹

2004

J. Phys. A: Math. Gen.

106

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We present improved simulations of three-dimensional self avoiding walks with one end attached to an impenetrable surface on the simple cubic lattice. This surface can either be a-thermal, having thus only an entropic effect, or attractive. In the latter case we concentrate on the adsorption transition, We find clear evidence for the cross-over exponent to be smaller than 1/2, in contrast to all previous simulations but in agreement with a re-summed field theoretic ǫ-expansion. Since we use the pruned-enriched Rosenbluth method (PERM) which allows very precise estimates of the partition sum itself, we also obtain improved estimates for all entropic critical exponents.

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Section: Results: A-thermal Wallssupporting

confidence: 76%

Simulations of grafted polymers in a good solvent

Grassberger¹

2004

J. Phys. A: Math. Gen.

106

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“…In our model the two arms of the chromosomes carrying the gene loci are represented by two polymer chains. These chains are built up of ellipsoidal monomer segments with a ratio of 1 20 between the half-axis (for a detailed description of the physical model used see 5 ). The chains have to be non-ideal, because the chromosomes cannot penetrate one another.…”

Section: The Modelmentioning

confidence: 99%

MODELLING OF POLYCOMB-DEPENDENT CHROMOSOMAL INTERACTIONS INVOLVED IN DROSOPHILA GENE SILENCING

Ritter

Odenheimer

Heermann

et al. 2006

Biophys. Rev. Lett.

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The conditions of the chromosomes inside the nucleus in the Rabl configuration have been modelled as self-avoiding polymer chains under restraining conditions. To ensure that the chromosomes remain stretched out and lined up, we fixed their end points to two opposing walls. The numbers of segments N, the distances d1 and d2 between the fixpoints, and the wall-to-wall distance z (as measured in segment lengths) determine an approximate value for the Kuhn segment length kl. We have simulated the movement of the chromosomes using molecular dynamics to obtain the expected distance distribution between the genetic loci in the absence of further attractive or repulsive forces. A comparison to biological experiments on Drosophila Melanogaster yields information on the parameters for our model. With the correct parameters it is possible to draw conclusions on the strength and range of the attraction that leads to pairing.

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“…More involved calculations include computation of the full partition function under confinement and its derivative with respect to displacement [7]. Alternatively, this force can be calculated from the local concentration of mass points near the surface [8,9]. For a chain tethered to a hard wall, the force increases with chain length, but saturates at ∼ k B T /a.…”

Section: Introductionmentioning

confidence: 99%

Calculation of a fluctuating entropic force by phase space sampling

Waters

Kim

2015

Phys. Rev. E

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A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.

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Forces by and on a Polymer Grafted to a Repulsive Wall

Cited by 3 publications

References 26 publications

Simulations of grafted polymers in a good solvent

Simulations of grafted polymers in a good solvent

MODELLING OF POLYCOMB-DEPENDENT CHROMOSOMAL INTERACTIONS INVOLVED IN DROSOPHILA GENE SILENCING

Calculation of a fluctuating entropic force by phase space sampling

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