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Affiliation(s)
- Karthik Nagarajan
- K. Nagarajan, Prof. S. B. ChenDepartment of Chemical & Biomolecular EngineeringNational University of Singapore Singapore 117585 Singapore
| | - Shing Bor Chen
- K. Nagarajan, Prof. S. B. ChenDepartment of Chemical & Biomolecular EngineeringNational University of Singapore Singapore 117585 Singapore
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2
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Wang C, Wu F, Zhao B, Chen YC, Luo MB. Spontaneous Injection of Polymer into a Spherical Cavity from a Narrow Tube. Macromolecules 2020. [DOI: 10.1021/acs.macromol.9b02645] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Chao Wang
- Department of Physics, Taizhou University, Taizhou 318000, China
| | - Fan Wu
- Department of Physics, Taizhou University, Taizhou 318000, China
| | - Bin Zhao
- Department of Physics, Taizhou University, Taizhou 318000, China
| | - Ying-Cai Chen
- Department of Physics, Taizhou University, Taizhou 318000, China
| | - Meng-Bo Luo
- Department of Physics, Zhejiang University, Hangzhou 310027, China
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3
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Polson JM, Heckbert DR. Polymer translocation into cavities: Effects of confinement geometry, crowding, and bending rigidity on the free energy. Phys Rev E 2019; 100:012504. [PMID: 31499877 DOI: 10.1103/physreve.100.012504] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Indexed: 06/10/2023]
Abstract
Monte Carlo simulations are used to study the translocation of a polymer into a cavity. Modeling the polymer as a hard-sphere chain with a length up to N=601 monomers, we use a multiple-histogram method to measure the variation of the conformational free energy of the polymer with respect to the number of translocated monomers. The resulting free-energy functions are then used to obtain the confinement free energy for the translocated portion of the polymer. We characterize the confinement free energy for a flexible polymer in cavities with constant cross-sectional area A for various cavity shapes (cylindrical, rectangular, and triangular) as well as for tapered cavities with pyramidal and conical shape. The scaling of the free energy with cavity volume and translocated polymer subchain length is generally consistent with predictions from simple scaling arguments, with small deviations in the scaling exponents likely due to finite-size effects. The confinement free energy depends strongly on cavity shape anisometry and is a minimum for an isometric cavity shape with a length-to-width ratio of unity. Entropic depletion at the edges or vertices of the confining cavity are evident in the results for constant-A and pyramidal cavities. For translocation into infinitely long cones, the scaling of the free energy with taper angle is consistent with a theoretical prediction employing the blob model. We also examine the effects of polymer bending rigidity on the translocation free energy for cylindrical cavities. For isometric cavities, the observed scaling behavior is in partial agreement with theoretical predictions, with discrepancies arising from finite-size effects that prevent the emergence of well-defined scaling regimes. In addition, translocation into highly anisometric cylindrical cavities leads to a multistage folding process for stiff polymers. Finally, we examine the effects of crowding agents inside the cavity. We find that the confinement free energy increases with crowder density. At constant packing fraction the magnitude of this effect lessens with increasing crowder size for a crowder-to-monomer size ratio ≥1.
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Affiliation(s)
- James M Polson
- Department of Physics, University of Prince Edward Island, 550 University Avenue, Charlottetown, Prince Edward Island, Canada C1A 4P3
| | - David R Heckbert
- Department of Physics, University of Prince Edward Island, 550 University Avenue, Charlottetown, Prince Edward Island, Canada C1A 4P3
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4
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Sun LZ, Wang CH, Luo MB, Li H. Trapped and non-trapped polymer translocations through a spherical pore. J Chem Phys 2019; 150:024904. [PMID: 30646715 DOI: 10.1063/1.5063331] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The polymer translocation through a spherical pore is studied using the Langevin dynamics simulation. The translocation events are classified into two types: one is the trapped translocation in which the entire polymer is trapped in the pore and the other is the non-trapped translocation where the pore cannot hold the whole polymer. We find that the trapped translocation is favored at large spheres and small external voltages. However, the monomer-pore attraction would lead to the non-monotonic behavior of the trapped translocation possibility out of all translocation events. Moreover, both the trapped and non-trapped translocation times are dependent on the polymer length, pore size, external voltage, and the monomer-pore attraction. There exist two pathways for the polymer in the trapped translocation: an actively trapped pathway for the polymer trapped in the pore before the head monomer arrives at the pore exit, and a passively trapped pathway for the polymer trapped in the pore while the head monomer is struggling to move out of the pore. The studies of trapped pathways can provide a deep understanding of the polymer translocation behavior.
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Affiliation(s)
- Li-Zhen Sun
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
| | - Chang-Hui Wang
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
| | - Meng-Bo Luo
- Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Haibin Li
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
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5
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The role of ion partitioning in electrohydrodynamic characteristics of soft nanofluidics: Inclusion of EDL overlap and steric effects. Chem Eng Sci 2018. [DOI: 10.1016/j.ces.2018.05.049] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
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6
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Sun LZ, Luo MB, Cao WP, Li H. Theoretical study on the polymer translocation into an attractive sphere. J Chem Phys 2018; 149:024901. [PMID: 30007381 DOI: 10.1063/1.5025609] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
We report a non-sampling model, combining the blob method with the standard lattice-based approximation, to calculate the free energy for the polymer translocation into an attractive sphere (i.e., spherical confined trans side) through a small pore. The translocation time is then calculated by the Fokker-Planck equation based on the free energy profile. There is a competition between the confinement effect of the sphere and the polymer-sphere attraction. The translocation time is increased due to the confinement effect of the sphere, whereas it is reduced by the polymer-sphere attraction. The two effects offset each other at a special polymer-sphere attraction which is dependent on the sphere size, the polymer length, and the driving force. Moreover, the entire translocation process can be divided into an uncrowded stage where the polymer does not experience the confinement effect of the sphere and a crowded stage where the polymer is confined by the sphere. At the critical sphere radius, the durations of the two (uncrowded and crowded) stages are the same. The critical sphere radius R* has a scaling relation with the polymer length N as R* ∼ Nβ. The calculation results show that the current model can effectively treat the translocation of a three-dimensional self-avoiding polymer into the spherical confined trans side.
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Affiliation(s)
- Li-Zhen Sun
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
| | - Meng-Bo Luo
- Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Wei-Ping Cao
- Institute of Optoelectronic Technology, Lishui University, Lishui 323000, China
| | - Haibin Li
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
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7
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The Semiflexible Polymer Translocation into Laterally Unbounded Region between Two Parallel Flat Membranes. Polymers (Basel) 2016; 8:polym8090332. [PMID: 30974609 PMCID: PMC6431992 DOI: 10.3390/polym8090332] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2016] [Revised: 08/28/2016] [Accepted: 08/30/2016] [Indexed: 11/17/2022] Open
Abstract
Using the dynamic Monte Carlo method, we investigate dynamics of semiflexible polymer translocation through a nanopore into laterally unbounded region between two parallel flat membranes with separation R in presence of an electric field inside the pore. The average translocation time τ initially decreases rapidly with increase of R in the range of R < 10 and then almost keeps constant for R ≥ 10, and the decline range increases with increase of dimensionless bending stiffness κ. We mainly study the effect of chain length N, κ and electric field strength E on the translocation process for R = 5. The translocation dynamics is significantly altered in comparison to an unconfined environment. We find τ ~ Nα, where the exponent α increases with increase of E for small κ. α initially increases slowly with increase of E and then keeps constant for moderate κ. α decreases with increase of E for large κ. However, α decreases with increase of κ under various E. In addition, we find τ ~ κβ. β decreases with increase of N under various E. These behaviors are interpreted in terms of the probability distribution of translocation time and the waiting time of an individual monomer segment passing through the pore during translocation.
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8
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Cao Q, Bachmann M. Impact of surface charge density and motor force upon polyelectrolyte packaging in viral capsids. ACTA ACUST UNITED AC 2016. [DOI: 10.1002/polb.24019] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Qianqian Cao
- College of Mechanical and Electrical EngineeringJiaxing UniversityJiaxing314001 People's Republic of China
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of GeorgiaAthens Georgia30602
- Institut für Theoretische Physik, Freie Universität BerlinArnimallee 1414195Berlin Germany
| | - Michael Bachmann
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of GeorgiaAthens Georgia30602
- Instituto de Física, Universidade Federal de Mato Grosso78060‐900Cuiabá (MT) Brazil
- Departamento de FísicaUniversidade Federal de Minas Gerais31270‐901Belo Horizonte (MG) Brazil
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Polson JM. Polymer translocation into and out of an ellipsoidal cavity. J Chem Phys 2015; 142:174903. [DOI: 10.1063/1.4919642] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- James M. Polson
- Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island C1A 4P3, Canada
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10
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Palyulin VV, Ala-Nissila T, Metzler R. Polymer translocation: the first two decades and the recent diversification. SOFT MATTER 2014; 10:9016-37. [PMID: 25301107 DOI: 10.1039/c4sm01819b] [Citation(s) in RCA: 139] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.
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Affiliation(s)
- Vladimir V Palyulin
- Institute for Physics & Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany.
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11
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Zhang K, Luo K. Polymer translocation into a confined space: Influence of the chain stiffness and the shape of the confinement. J Chem Phys 2014; 140:094902. [DOI: 10.1063/1.4867239] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Polson JM, McCaffrey ACM. Polymer translocation dynamics in the quasi-static limit. J Chem Phys 2013; 138:174902. [PMID: 23656154 DOI: 10.1063/1.4803022] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Monte Carlo (MC) simulations are used to study the dynamics of polymer translocation through a nanopore in the limit where the translocation rate is sufficiently slow that the polymer maintains a state of conformational quasi-equilibrium. The system is modeled as a flexible hard-sphere chain that translocates through a cylindrical hole in a hard flat wall. In some calculations, the nanopore is connected at one end to a spherical cavity. Translocation times are measured directly using MC dynamics simulations. For sufficiently narrow pores, translocation is sufficiently slow that the mean translocation time scales with polymer length N according to <τ> ∝ (N - N(p))(2), where N(p) is the average number of monomers in the nanopore; this scaling is an indication of a quasi-static regime in which polymer-nanopore friction dominates. We use a multiple-histogram method to calculate the variation of the free energy with Q, a coordinate used to quantify the degree of translocation. The free energy functions are used with the Fokker-Planck formalism to calculate translocation time distributions in the quasi-static regime. These calculations also require a friction coefficient, characterized by a quantity N(eff), the effective number of monomers whose dynamics are affected by the confinement of the nanopore. This was determined by fixing the mean of the theoretical distribution to that of the distribution obtained from MC dynamics simulations. The theoretical distributions are in excellent quantitative agreement with the distributions obtained directly by the MC dynamics simulations for physically meaningful values of N(eff). The free energy functions for narrow-pore systems exhibit oscillations with an amplitude that is sensitive to the nanopore length. Generally, larger oscillation amplitudes correspond to longer translocation times.
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Affiliation(s)
- James M Polson
- Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island C1A 4P3, Canada
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Das S, Guha A, Mitra SK. Exploring new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with overlapping electric double layers. Anal Chim Acta 2013; 804:159-66. [PMID: 24267077 DOI: 10.1016/j.aca.2013.09.061] [Citation(s) in RCA: 61] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2013] [Revised: 09/04/2013] [Accepted: 09/28/2013] [Indexed: 10/26/2022]
Abstract
In this paper, we unravel new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with thick overlapping Electric Double Layers (EDLs). We observe that the streaming potential, for a given value of the capillary zeta (ζ) potential, varies with the EDL thickness and a dimensionless parameter R, quantifying the conduction current. Depending on the value of R, variation of the streaming potential with the EDL thickness demonstrates distinct scaling regimes: one can witness a Quadratic Regime where the streaming potential varies as the square of the EDL thickness, a Weak Regime where the streaming potential shows a weaker variation with the EDL thickness, and a Saturation Regime where the streaming potential ceases to vary with the EDL thickness. Effective viscosity, characterizing the electroviscous effect, obeys the variation of the streaming potential for smaller EDL thickness values; however, for larger EDL thickness the electroosmotic flow profile dictates the electroviscous effect, with insignificant contribution of the streaming potential.
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Affiliation(s)
- Siddhartha Das
- Micro and Nanoscale Transport Laboratory, Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8
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Polson JM, Hassanabad MF, McCaffrey A. Simulation study of the polymer translocation free energy barrier. J Chem Phys 2013; 138:024906. [DOI: 10.1063/1.4774118] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Lee PH, Helms V, Geyer T. Coarse-grained Brownian dynamics simulations of protein translocation through nanopores. J Chem Phys 2012; 137:145105. [DOI: 10.1063/1.4757265] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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