1
|
Castro-Villarreal P, Ramírez JE. Stochastic curvature of enclosed semiflexible polymers. Phys Rev E 2019; 100:012503. [PMID: 31499867 DOI: 10.1103/physreve.100.012503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2018] [Indexed: 11/07/2022]
Abstract
The conformational states of a semiflexible polymer enclosed in a compact domain of typical size a are studied as stochastic realizations of paths defined by the Frenet equations under the assumption that stochastic "curvature" satisfies a white noise fluctuation theorem. This approach allows us to derive the Hermans-Ullman equation, where we exploit a multipolar decomposition that allows us to show that the positional probability density function is well described by a telegrapher's equation whenever 2a/ℓ_{p}>1, where ℓ_{p} is the persistence length. We also develop a Monte Carlo algorithm for use in computer simulations in order to study the conformational states in a compact domain. In addition, the case of a semiflexible polymer enclosed in a square domain of side a is presented as an explicit example of the formulated theory and algorithm. In this case, we show the existence of a polymer shape transition similar to the one found by Spakowitz and Wang [Phys. Rev. Lett. 91, 166102 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.166102] where in this case the critical persistence length is ℓ_{p}^{*}≃a/8 such that the mean-square end-to-end distance exhibits an oscillating behavior for values ℓ_{p}>ℓ_{p}^{*}, whereas for ℓ_{p}<ℓ_{p}^{*} it behaves monotonically increasing.
Collapse
Affiliation(s)
- Pavel Castro-Villarreal
- Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas, Carretera Emiliano Zapata, Km. 8, Rancho San Francisco, 29050 Tuxtla Gutiérrez, Chiapas, Mexico
| | - J E Ramírez
- Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 165, 72000 Puebla, Puebla, Mexico.,Departamento de Física de Partículas, Universidad de Santiago de Compostela, E-15782 Santiago de Compostela, Spain
| |
Collapse
|
2
|
Sharma KK, Marzinek JK, Tantirimudalige SN, Bond PJ, Wohland T. Single-molecule studies of flavivirus envelope dynamics: Experiment and computation. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2018; 143:38-51. [PMID: 30223001 DOI: 10.1016/j.pbiomolbio.2018.09.001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Revised: 09/06/2018] [Accepted: 09/11/2018] [Indexed: 12/11/2022]
Abstract
Flaviviruses are simple enveloped viruses exhibiting complex structural and functional heterogeneities. Decades of research have provided crucial basic insights, antiviral medication and moderately successful gene therapy trials. The most infectious particle is, however, not always the most abundant one in a population, questioning the utility of classic ensemble-averaging virology approaches. Indeed, viral replication is often not particularly efficient, prone to errors or containing parallel routes. Here, we review different single-molecule sensitive fluorescence methods that are employed to investigate flaviviruses. In particular, we review how (i) time-resolved Förster resonance energy transfer (trFRET) was applied to probe dengue envelope conformations; (ii) FRET-fluorescence correlation spectroscopy to investigate dengue envelope intrinsic dynamics and (iii) single particle tracking to follow the path of dengue viruses in cells. We also discuss how such methods may be supported by molecular dynamics (MD) simulations over a range of spatio-temporal scales, to provide complementary data on the structure and dynamics of flaviviral systems. We describe recent improvements in multiscale MD approaches that allowed the simulation of dengue particle envelopes in near-atomic resolution. We hope this review is an incentive for setting up and applying similar single-molecule studies and combine them with MD simulations to investigate structural dynamics of entire flavivirus particles over the nanosecond-to-millisecond time-scale and follow viruses during infection in cells over milliseconds to minutes.
Collapse
Affiliation(s)
- Kamal Kant Sharma
- Department of Biological Sciences, National University of Singapore, 14 Science Drive 4, Singapore 117543, Singapore
| | - Jan K Marzinek
- Department of Biological Sciences, National University of Singapore, 14 Science Drive 4, Singapore 117543, Singapore; Bioinformatics Institute (A*STAR), 30 Biopolis Street, #07-01 Matrix, Singapore 138671, Singapore
| | - Sarala Neomi Tantirimudalige
- Department of Biological Sciences, National University of Singapore, 14 Science Drive 4, Singapore 117543, Singapore
| | - Peter J Bond
- Department of Biological Sciences, National University of Singapore, 14 Science Drive 4, Singapore 117543, Singapore; Bioinformatics Institute (A*STAR), 30 Biopolis Street, #07-01 Matrix, Singapore 138671, Singapore.
| | - Thorsten Wohland
- Department of Biological Sciences, National University of Singapore, 14 Science Drive 4, Singapore 117543, Singapore; Department of Chemistry, National University of Singapore, 14 Science Drive 4, Singapore 117543, Singapore; Centre for Bioimaging Sciences, National University of Singapore, 14 Science Drive 4, Singapore 117557, Singapore.
| |
Collapse
|
3
|
Smith GR, Xie L, Schwartz R. Modeling Effects of RNA on Capsid Assembly Pathways via Coarse-Grained Stochastic Simulation. PLoS One 2016; 11:e0156547. [PMID: 27244559 PMCID: PMC4887116 DOI: 10.1371/journal.pone.0156547] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2015] [Accepted: 05/16/2016] [Indexed: 12/02/2022] Open
Abstract
The environment of a living cell is vastly different from that of an in vitro reaction system, an issue that presents great challenges to the use of in vitro models, or computer simulations based on them, for understanding biochemistry in vivo. Virus capsids make an excellent model system for such questions because they typically have few distinct components, making them amenable to in vitro and modeling studies, yet their assembly can involve complex networks of possible reactions that cannot be resolved in detail by any current experimental technology. We previously fit kinetic simulation parameters to bulk in vitro assembly data to yield a close match between simulated and real data, and then used the simulations to study features of assembly that cannot be monitored experimentally. The present work seeks to project how assembly in these simulations fit to in vitro data would be altered by computationally adding features of the cellular environment to the system, specifically the presence of nucleic acid about which many capsids assemble. The major challenge of such work is computational: simulating fine-scale assembly pathways on the scale and in the parameter domains of real viruses is far too computationally costly to allow for explicit models of nucleic acid interaction. We bypass that limitation by applying analytical models of nucleic acid effects to adjust kinetic rate parameters learned from in vitro data to see how these adjustments, singly or in combination, might affect fine-scale assembly progress. The resulting simulations exhibit surprising behavioral complexity, with distinct effects often acting synergistically to drive efficient assembly and alter pathways relative to the in vitro model. The work demonstrates how computer simulations can help us understand how assembly might differ between the in vitro and in vivo environments and what features of the cellular environment account for these differences.
Collapse
Affiliation(s)
- Gregory R. Smith
- Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
| | - Lu Xie
- Joint Carnegie Mellon/University of Pittsburgh Ph.D. Program in Computational Biology, Pittsburgh, Pennsylvania, United States of America
- Computational Biology Department, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
| | - Russell Schwartz
- Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- Computational Biology Department, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- * E-mail:
| |
Collapse
|
4
|
|
5
|
Angelescu DG, Linse P. Branched-linear polyion complexes at variable charge densities. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:355101. [PMID: 26249029 DOI: 10.1088/0953-8984/27/35/355101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Structural behavior of complexes formed by a charged and branched copolymer and an oppositely charged and linear polyion was examined by Monte Carlo simulations employing a coarse-grained bead-spring model. The fractional bead charge and the branching density were systematically varied; the former between 0e and 1e and the latter such that both the comb-polymer and the bottle-brush limits were included. The number of beads of the main chain of the branched copolymer and of the linear polyion was always kept constant and equal, and a single side-chain length was used. Our analysis involved characterization of the complex as well as investigation of size, shape, and flexibility of the charged moieties. An interplay between Coulomb interaction and side-chain repulsion governed the structure of the polyion complex. At strong Coulomb interaction, the complexes underwent a gradual transition from a globular structure at low branching density to an extended one at high branching density. As the electrostatic coupling was decreased, the transition was smoothened and shifted to lower branching density, and, eventually, a behavior similar to that found for neutral branched polymer was observed. Structural analogies and dissimilarities with uncharged branched polymers in poor solutions are discussed.
Collapse
Affiliation(s)
- Daniel G Angelescu
- Romanian Academy, Institute of Physical Chemistry Ilie Murgulescu, Splaiul Independentei 202, 060021 Bucharest, Romania
| | | |
Collapse
|
6
|
Jurij R, Per L. MOLSIM: A modular molecular simulation software. J Comput Chem 2015; 36:1259-74. [PMID: 25994597 PMCID: PMC5033024 DOI: 10.1002/jcc.23919] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2015] [Revised: 03/23/2015] [Accepted: 03/26/2015] [Indexed: 11/06/2022]
Abstract
The modular software MOLSIM for all-atom molecular and coarse-grained simulations is presented with focus on the underlying concepts used. The software possesses four unique features: (1) it is an integrated software for molecular dynamic, Monte Carlo, and Brownian dynamics simulations; (2) simulated objects are constructed in a hierarchical fashion representing atoms, rigid molecules and colloids, flexible chains, hierarchical polymers, and cross-linked networks; (3) long-range interactions involving charges, dipoles and/or anisotropic dipole polarizabilities are handled either with the standard Ewald sum, the smooth particle mesh Ewald sum, or the reaction-field technique; (4) statistical uncertainties are provided for all calculated observables. In addition, MOLSIM supports various statistical ensembles, and several types of simulation cells and boundary conditions are available. Intermolecular interactions comprise tabulated pairwise potentials for speed and uniformity and many-body interactions involve anisotropic polarizabilities. Intramolecular interactions include bond, angle, and crosslink potentials. A very large set of analyses of static and dynamic properties is provided. The capability of MOLSIM can be extended by user-providing routines controlling, for example, start conditions, intermolecular potentials, and analyses. An extensive set of case studies in the field of soft matter is presented covering colloids, polymers, and crosslinked networks.
Collapse
Affiliation(s)
- Reščič Jurij
- Department of Physical Chemistry, Faculty of Chemistry and Chemical Technology, University of Ljubljana, PO Box 537, SI-1001, Ljubljana, Slovenia
| | - Linse Per
- Department of Chemistry, Physical Chemistry, Lund University, PO Box 124, SE-221 00, Lund, Sweden
| |
Collapse
|
7
|
Abstract
I present a review of the theoretical and computational methodologies that have been used to model the assembly of viral capsids. I discuss the capabilities and limitations of approaches ranging from equilibrium continuum theories to molecular dynamics simulations, and I give an overview of some of the important conclusions about virus assembly that have resulted from these modeling efforts. Topics include the assembly of empty viral shells, assembly around single-stranded nucleic acids to form viral particles, and assembly around synthetic polymers or charged nanoparticles for nanotechnology or biomedical applications. I present some examples in which modeling efforts have promoted experimental breakthroughs, as well as directions in which the connection between modeling and experiment can be strengthened.
Collapse
|
8
|
Synthesis and modeling of calcium alginate nanoparticles in quaternary water-in-oil microemulsions. Colloids Surf A Physicochem Eng Asp 2014. [DOI: 10.1016/j.colsurfa.2014.01.083] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
9
|
Gao J, Tang P, Yang Y, Chen JZY. Free energy of a long semiflexible polymer confined in a spherical cavity. SOFT MATTER 2014; 10:4674-4685. [PMID: 24839199 DOI: 10.1039/c4sm00605d] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The free energy and conformational properties of a wormlike chain confined inside a spherical surface are investigated. We show that in the weak-confinement limit, the wormlike chain model exactly reproduces the confinement properties of a Gaussian chain; in such a case the confinement entropy dominates the free energy; in the strong-confinement limit, the free energy is dominated by the bending energy of the chain, which is forced to wrap around the confining surface. We also present a numerical solution within the crossover region between the two limits, solving the differential equation that the probability distribution function satisfies.
Collapse
Affiliation(s)
- Jie Gao
- Department of Macromolecular Science, Fudan University, Shanghai 200433, China.
| | | | | | | |
Collapse
|
10
|
Sun T, Yang Z. Coil–helix transition of biopolymer confined in finite cylinder. Chem Phys Lett 2014. [DOI: 10.1016/j.cplett.2014.05.081] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
11
|
Fathizadeh A, Heidari M, Eslami-Mossallam B, Ejtehadi MR. Confinement dynamics of a semiflexible chain inside nano-spheres. J Chem Phys 2013; 139:044912. [PMID: 23902024 DOI: 10.1063/1.4816626] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
We study the conformations of a semiflexible chain, confined in nano-scaled spherical cavities, under two distinct processes of confinement. Radial contraction and packaging are employed as two confining procedures. The former method is performed by gradually decreasing the diameter of a spherical shell which envelopes a confined chain. The latter procedure is carried out by injecting the chain inside a spherical shell through a hole on the shell surface. The chain is modeled with a rigid body molecular dynamics simulation and its parameters are adjusted to DNA base-pair elasticity. Directional order parameter is employed to analyze and compare the confined chain and the conformations of the chain for two different sizes of the spheres are studied in both procedures. It is shown that for the confined chains in the sphere sizes of our study, they appear in spiral or tennis-ball structures, and the tennis-ball structure is more likely to be observed in more compact confinements. Our results also show that the dynamical procedure of confinement and the rate of the confinement are influential parameters of the structure of the chain inside spherical cavities.
Collapse
Affiliation(s)
- A Fathizadeh
- Sharif University of Technology, Institute for Nanoscience and Nanotechnology, P.O. Box 14588-89694, Tehran, Iran
| | | | | | | |
Collapse
|
12
|
Liang Q, Li J, Zhang P, Chen JZY. Modified diffusion equation for the wormlike-chain statistics in curvilinear coordinates. J Chem Phys 2013; 138:244910. [PMID: 23822277 DOI: 10.1063/1.4811515] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Qin Liang
- School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, People's Republic of China
| | | | | | | |
Collapse
|
13
|
Strong and Weak Polyelectrolyte Adsorption onto Oppositely Charged Curved Surfaces. POLYELECTROLYTE COMPLEXES IN THE DISPERSED AND SOLID STATE I 2013. [DOI: 10.1007/12_2012_183] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
|
14
|
Zhang D, Yang Z, Wen X, Xiang Z, He L, Ran S, Zhang L. Helical Conformations of Semiflexible Polymers Confined between Two Concentric Cylinders. J Phys Chem B 2011; 115:14333-40. [DOI: 10.1021/jp204722g] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Dong Zhang
- Departmemt of Physics, Zhejiang University, Hangzhou 310027, China
| | - Zhiyong Yang
- Departmemt of Physics, Zhejiang University, Hangzhou 310027, China
| | - Xiaohui Wen
- Departmemt of Physics, Zhejiang University, Hangzhou 310027, China
| | - Zhangheng Xiang
- Departmemt of Physics, Zhejiang University, Hangzhou 310027, China
| | - Linli He
- Departmemt of Physics, Wenzhou University, Wenzhou 325035, China
| | - Shiyong Ran
- Departmemt of Physics, Wenzhou University, Wenzhou 325035, China
| | - Linxi Zhang
- Departmemt of Physics, Wenzhou University, Wenzhou 325035, China
| |
Collapse
|
15
|
Oskolkov NN, Linse P, Potemkin II, Khokhlov AR. Nematic ordering of polymers in confined geometry applied to DNA packaging in viral capsids. J Phys Chem B 2010; 115:422-32. [PMID: 21186830 DOI: 10.1021/jp108461z] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A density functional theory of the spatial distribution and biaxial nematic order of polymers of arbitrary length and rigidity inside a spherical cavity is proposed. The local order of different chain segments is considered as an alignment to a spatially varying director field of cylindrical symmetry. The steric interactions are taken into account in the second virial approximation. Polymer density and orientational order distributions inside the spherically cavity are the principal results. It was found that short and flexible polymers were located at the center of the sphere and were orientationaly disordered. Upon increasing polymer length and/or polymer rigidity, the location of the polymer was continuously shifted toward the surface of the spherical cavity and the polymer segments became gradually more aligned. Parameters have been selected to model the behavior of genomes in spherical viral capsids.
Collapse
Affiliation(s)
- Nikolay N Oskolkov
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, USA.
| | | | | | | |
Collapse
|
16
|
Abstract
The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated with encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids.
Collapse
Affiliation(s)
- Oren M Elrad
- Department of Physics, Brandeis University, Waltham, MA, USA
| | | |
Collapse
|
17
|
Mechanisms of capsid assembly around a polymer. Biophys J 2010; 99:619-28. [PMID: 20643082 DOI: 10.1016/j.bpj.2010.04.035] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2010] [Revised: 04/13/2010] [Accepted: 04/15/2010] [Indexed: 11/23/2022] Open
Abstract
Capsids of many viruses assemble around nucleic acids or other polymers. Understanding how the properties of the packaged polymer affect the assembly process could promote biomedical efforts to prevent viral assembly or nanomaterials applications that exploit assembly. To this end, we simulate on a lattice the dynamical assembly of closed, hollow shells composed of several hundred to 1000 subunits, around a flexible polymer. We find that assembly is most efficient at an optimum polymer length that scales with the surface area of the capsid; polymers that are significantly longer than optimal often lead to partial-capsids with unpackaged polymer "tails" or a competition between multiple partial-capsids attached to a single polymer. These predictions can be tested with bulk experiments in which capsid proteins assemble around homopolymeric RNA or synthetic polyelectrolytes. We also find that the polymer can increase the net rate of subunit accretion to a growing capsid both by stabilizing the addition of new subunits and by enhancing the incoming flux of subunits; the effects of these processes may be distinguishable with experiments that monitor the assembly of individual capsids.
Collapse
|
18
|
Alben S. Packings of a charged line on a sphere. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:066603. [PMID: 19256964 DOI: 10.1103/physreve.78.066603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2008] [Indexed: 05/27/2023]
Abstract
We find equilibrium configurations of open and closed lines of charge on a sphere, and track them with respect to varying sphere radius. Closed lines transition from a circle to a spiral-like shape through two low-wave-number bifurcations-"baseball seam" and "twist"-which minimize Coulomb energy. The spiral shape is the unique stable equilibrium of the closed line. Other unstable equilibria arise through tip-splitting events. An open line transitions smoothly from an arc of a great circle to a spiral as the sphere radius decreases. Under repulsive potentials with faster-than-Coulomb power-law decay, the spiral is tighter in initial stages of sphere shrinkage, but at later stages of shrinkage the equilibria for all repulsive potentials converge on a spiral with uniform spacing between turns. Multiple stable equilibria of the open line are observed.
Collapse
Affiliation(s)
- Silas Alben
- School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160, USA.
| |
Collapse
|