scholarly journals Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections

Polymers ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2050
Author(s):  
Ming Li ◽  
Jizeng Wang
Keyword(s):  
Cross Sections ◽  
Brownian Dynamics ◽  
Statistical Physics ◽  
Polymer Chains ◽  
Chain Model ◽  
Mode Decomposition ◽  
Dynamics Simulations ◽  
Single Formula ◽  
Wormlike Chain Model ◽  
Confined Polymer Chains

We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. This single formula was generalized to be valid for tube confinements with arbitrary cross-sections. In addition, we extended the generalized bead-rod model for Brownian dynamics simulations of confined polymer chains subjected to force stretching, so that the confinement effects to the chains applied by the tubes with arbitrary cross-sections can be quantitatively taken into account through numerical simulations. Extensive simulation examples on the wormlike chains confined in tubes of various shapes quantitatively justified the theoretically derived generalized formula on the force-confinement-extension relation of the chains.

scholarly journals Statistical Behaviors of Semiflexible Polymer Chains Stretched in Rectangular Tubes

Polymers ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 260 ◽  
Author(s):  
Jizeng Wang ◽  
Kai Li
Keyword(s):  
Brownian Dynamics ◽  
Numerical Solutions ◽  
Persistence Length ◽  
Polymer Chains ◽  
Chain Model ◽  
Semiflexible Polymer ◽  
Dynamics Simulations ◽  
Wormlike Chain Model ◽  
Deflection Theory ◽  
Brownian Dynamics Simulations

We investigated the statistical behaviors of semiflexible polymer chains, which were simultaneously subjected to force stretching and rectangular tube confinement. Based on the wormlike chain model and Odijk deflection theory, we derived a new deflection length, by using which new compact formulas were obtained for the confinement free energy and force–confinement–extension relations. These newly derived formulas were justified by numerical solutions of the eigenvalue problem associated with the Fokker–Planck governing equation and extensive Brownian dynamics simulations based on the so-called generalized bead-rod (GBR) model. We found that, compared to classical deflection theory, these new formulas were valid for a much more extended range of the confinement size/persistence length ratio and had no adjustable fitting parameters for sufficiently long semiflexible chains in the whole deflection regime.

scholarly journals Statistical Behaviours of Semiflexible Polymer Chains Stretched in Rectangular Tubes

2018 ◽  
Author(s):  
Jizeng Wang ◽  
Kai Li
Keyword(s):  
Brownian Dynamics ◽  
Numerical Solutions ◽  
Persistence Length ◽  
Polymer Chains ◽  
Chain Model ◽  
Semiflexible Polymer ◽  
Dynamics Simulations ◽  
Wormlike Chain Model ◽  
Deflection Theory ◽  
Brownian Dynamics Simulations

We quantitatively investigated the statistical behaviors of semiflexible polymer chains, which are simultaneously subjected to force stretching and rectangular tube confinement. Based on the wormlike chain model and Odijk deflection theory, we derived a new deflection length, by which new compact formulas are obtained for the confinement free energy and force-confinement-extension relation. These newly derived formulas have been justified by numerical solutions of an eigenvalue problem associated with the Fokker-Planck governing equation and extensive Brownian dynamics simulations based on the so-called Generalized Bead-Rod (GBR) model. We found that, comparing to the classical deflection theory, these new formulas are valid for a much extended range of the confinement-size /persistence-length ratio, and have no adjustable fitting parameters for sufficient long semiflexible chains in the whole deflection regime.

A Finite Element-Based Coarse-Grained Model for Cell–Nanomaterial Interactions by Combining Absolute Nodal Coordinate Formula and Brownian Dynamics

2020 ◽  
Vol 88 (4) ◽  
Author(s):  
Teng Ma ◽  
Yuanpeng Liu ◽  
Guochang Lin ◽  
Changguo Wang ◽  
Huifeng Tan
Keyword(s):  
Finite Element ◽  
Brownian Dynamics ◽  
Lipid Membrane ◽  
Contact Region ◽  
Detection Algorithm ◽  
Polymer Chains ◽  
Coarse Grained ◽  
Absolute Nodal Coordinate ◽  
Coarse Grained Model ◽  
Dynamics Simulations

Abstract A fundamental understanding of the interactions between one-dimensional nanomaterials and the cell membrane is of great importance for assessing the hazardous effects of viruses and improving the performance of drug delivery. Here, we propose a finite element-based coarse-grained model to describe the cell entry of nanomaterials based on an absolute nodal coordinate formula and Brownian dynamics. The interactions between nanoparticles and lipid membrane are described by the Lennard–Jones potential, and a contact detection algorithm is used to determine the contact region. Compared with the theoretical and published experimental results, the correctness of the model has been verified. We take two examples to test the robustness of the model: the endocytosis of nanorods grafted with polymer chains and simultaneous entry of multiple nanorods into a lipid membrane. It shows that the model can not only capture the effect of ligand–receptor binding on the penetration but also accurately characterize the cooperative or separate entry of multiple nanorods. This coarse-grained model is computationally highly efficient and will be powerful in combination with molecular dynamics simulations to provide an understanding of cell–nanomaterial interactions.

Extensional Response and Equilibrium Kinetics of Torsionally Relaxed dsDNA Under Tension: A Brownian Dynamics Study

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Ikenna D. Ivenso
Keyword(s):  
Single Molecule ◽  
Brownian Dynamics ◽  
Thermal Fluctuations ◽  
Aqueous Environment ◽  
Chain Model ◽  
Full Extension ◽  
Applied Tension ◽  
Dynamics Simulations ◽  
Kinetics Of ◽  
Insight Into

Deoxyribonucleic acid (DNA) is a long flexible polyelectrolyte that is housed in the aqueous environment within the cell of an organism. When a length of torsionally relaxed (untwisted) DNA is held in tension, such as is the case in many single molecule experiments, the thermal fluctuations arising from the constant bombardment of the DNA by the surrounding fluid molecules induce bending in it, while the applied tension tends to keep it extended. The combined effect of these influences is that DNA is never at its full extension but eventually attains an equilibrium value of end-to-end extension under these influences. An analytical model was developed to estimate the tension-dependent value of this extension. This model, however, does not provide any insight into the dynamics of the extensional response of DNA to applied tension nor the kinetics of DNA at equilibrium under said tension. This paper reports the results of Brownian dynamics simulations using a discrete wormlike-chain model of DNA that provide some insight into these dynamics and kinetics.

Shape of Confined Polymer Chains

1997 ◽  
Vol 7 (3) ◽  
pp. 433-447 ◽  
Author(s):  
C. E. Cordeiro ◽  
M. Molisana ◽  
D. Thirumalai
Keyword(s):  
Polymer Chains ◽  
Confined Polymer ◽  
Confined Polymer Chains

Quantitative Ranking of Ligand Binding Kinetics with a Multiscale Milestoning Simulation Approach

2018 ◽  
Author(s):  
Benjamin R. Jagger ◽  
Christoper T. Lee ◽  
Rommie Amaro
Keyword(s):  
Molecular Dynamics ◽  
Drug Discovery ◽  
Small Molecule ◽  
Brownian Dynamics ◽  
Model Simulation ◽  
Computational Cost ◽  
Lead Selection ◽  
Delta G ◽  
Dynamics Simulations

<p>The ranking of small molecule binders by their kinetic (kon and koff) and thermodynamic (delta G) properties can be a valuable metric for lead selection and optimization in a drug discovery campaign, as these quantities are often indicators of in vivo efficacy. Efficient and accurate predictions of these quantities can aid the in drug discovery effort, acting as a screening step. We have previously described a hybrid molecular dynamics, Brownian dynamics, and milestoning model, Simulation Enabled Estimation of Kinetic Rates (SEEKR), that can predict kon’s, koff’s, and G’s. Here we demonstrate the effectiveness of this approach for ranking a series of seven small molecule compounds for the model system, -cyclodextrin, based on predicted kon’s and koff’s. We compare our results using SEEKR to experimentally determined rates as well as rates calculated using long-timescale molecular dynamics simulations and show that SEEKR can effectively rank the compounds by koff and G with reduced computational cost. We also provide a discussion of convergence properties and sensitivities of calculations with SEEKR to establish “best practices” for its future use.</p>

scholarly journals Structure evolution of suspensions under time-dependent electric or magnetic field

2021 ◽  
Author(s):  
Konstantinos Manikas ◽  
Markus Hütter ◽  
Patrick D. Anderson
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Brownian Dynamics ◽  
Thermal Fluctuations ◽  
Time Dependent ◽  
Structure Evolution ◽  
Strength Increase ◽  
Large Rotation ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

AbstractThe effect of time-dependent external fields on the structures formed by particles with induced dipoles dispersed in a viscous fluid is investigated by means of Brownian Dynamics simulations. The physical effects accounted for are thermal fluctuations, dipole-dipole and excluded volume interactions. The emerging structures are characterised in terms of particle clusters (orientation, size, anisotropy and percolation) and network structure. The strength of the external field is increased in one direction and then kept constant for a certain amount of time, with the structure formation being influenced by the slope of the field-strength increase. This effect can be partially rationalized by inhomogeneous time re-scaling with respect to the field strength, however, the presence of thermal fluctuations makes the scaling at low field strength inappropriate. After the re-scaling, one can observe that the lower the slope of the field increase, the more network-like and the thicker the structure is. In the second part of the study the field is also rotated instantaneously by a certain angle, and the effect of this transition on the structure is studied. For small rotation angles ($$\theta \le 20^{{\circ }}$$ θ ≤ 20 ∘ ) the clusters rotate but stay largely intact, while for large rotation angles ($$\theta \ge 80^{{\circ }}$$ θ ≥ 80 ∘ ) the structure disintegrates and then reforms, due to the nature of the interactions (parallel dipoles with perpendicular inter-particle vector repel each other). For intermediate angles ($$20<\theta <80^{{\circ }}$$ 20 < θ < 80 ∘ ), it seems that, during rotation, the structure is altered towards a more network-like state, as a result of cluster fusion (larger clusters). The details provided in this paper concern an electric field, however, all results can be projected into the case of a magnetic field and paramagnetic particles.

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