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  1. Article ; Online: Exact expressions for the partition function of the one-dimensional Ising model in the fixed-M ensemble.

    Dantchev, Daniel / Rudnick, Joseph

    Physical review. E

    2022  Volume 106, Issue 4, Page(s) L042103

    Abstract: We obtain exact closed-form expressions for the partition function of the one-dimensional Ising model in the fixed-M ensemble, for three commonly used boundary conditions: periodic, antiperiodic, and Dirichlet. These expressions allow for the ... ...

    Abstract We obtain exact closed-form expressions for the partition function of the one-dimensional Ising model in the fixed-M ensemble, for three commonly used boundary conditions: periodic, antiperiodic, and Dirichlet. These expressions allow for the determination of fluctuation-induced forces in the canonical ensemble, which we term Helmholtz forces. The thermodynamic expressions and the calculations flowing from them should provide insights into the nature and behavior of fluctuation-induced forces in interesting and as-yet unexplored regimes.
    Language English
    Publishing date 2022-10-11
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.106.L042103
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  2. Article ; Online: Spanning tree model and the assembly kinetics of RNA viruses.

    Mizrahi, Inbal / Bruinsma, Robijn / Rudnick, Joseph

    Physical review. E

    2022  Volume 106, Issue 4-1, Page(s) 44405

    Abstract: Single-stranded RNA (ssRNA) viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization. However, ... ...

    Abstract Single-stranded RNA (ssRNA) viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization. However, during the self-assembly of complete viral particles in the cytoplasm of an infected cell, the viral genome molecules must be selected from a large pool of very similar host messenger RNA molecules and it is not known whether this also can be understood by free energy minimization. We address this question using a simple mathematical model, the spanning tree model, that was recently proposed for the assembly of small ssRNA viruses. We present a statistical physics analysis of the properties of this model. RNA selection takes place via a kinetic mechanism that operates during the formation of the nucleation complex and that is related to Hopfield kinetic proofreading.
    MeSH term(s) Virus Assembly ; Capsid Proteins/metabolism ; RNA Viruses ; RNA, Viral/metabolism ; Physics
    Chemical Substances Capsid Proteins ; RNA, Viral
    Language English
    Publishing date 2022-11-03
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.106.044405
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  3. Article ; Online: Packaging contests between viral RNA molecules and kinetic selectivity.

    Mizrahi, Inbal / Bruinsma, Robijn / Rudnick, Joseph

    PLoS computational biology

    2022  Volume 18, Issue 4, Page(s) e1009913

    Abstract: The paper presents a statistical-mechanics model for the kinetic selection of viral RNA molecules by packaging signals during the nucleation stage of the assembly of small RNA viruses. The effects of the RNA secondary structure and folding geometry of ... ...

    Abstract The paper presents a statistical-mechanics model for the kinetic selection of viral RNA molecules by packaging signals during the nucleation stage of the assembly of small RNA viruses. The effects of the RNA secondary structure and folding geometry of the packaging signals on the assembly activation energy barrier are encoded by a pair of characteristics: the wrapping number and the maximum ladder distance. Kinetic selection is found to be optimal when assembly takes place under conditions of supersaturation and also when the concentration ratio of capsid protein and viral RNA concentrations equals the stoichiometric ratio of assembled viral particles. As a function of the height of the activation energy barrier, there is a form of order-disorder transition such that for sufficiently low activation energy barriers, kinetic selectivity is erased by entropic effects associated with the number of assembly pathways.
    MeSH term(s) Capsid Proteins/chemistry ; Kinetics ; RNA Viruses ; RNA, Viral/chemistry ; Virus Assembly/physiology
    Chemical Substances Capsid Proteins ; RNA, Viral
    Language English
    Publishing date 2022-04-01
    Publishing country United States
    Document type Journal Article ; Research Support, U.S. Gov't, Non-P.H.S.
    ZDB-ID 2193340-6
    ISSN 1553-7358 ; 1553-734X
    ISSN (online) 1553-7358
    ISSN 1553-734X
    DOI 10.1371/journal.pcbi.1009913
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  4. Article ; Online: Invariant theory and orientational phase transitions.

    Rudnick, Joseph / Bruinsma, Robijn

    Physical review. E

    2019  Volume 100, Issue 1-1, Page(s) 12145

    Abstract: The Landau theory of phase transitions has been productively applied to phase transitions that involve rotational symmetry breaking, such as the transition from an isotropic fluid to a nematic liquid crystal. It even can be applied to the orientational ... ...

    Abstract The Landau theory of phase transitions has been productively applied to phase transitions that involve rotational symmetry breaking, such as the transition from an isotropic fluid to a nematic liquid crystal. It even can be applied to the orientational symmetry breaking of simple atomic or molecular clusters that are not true phase transitions. In this paper, we address fundamental problems that arise with the Landau theory when it is applied to rotational symmetry breaking transitions of more complex particle clusters that involve order parameters characterized by larger values of the l index of the dominant spherical harmonic that describes the broken symmetry state. The problems are twofold. First, one may encounter a thermodynamic instability of the expected ground state with respect to states with lower symmetry. A second problem concerns the proliferation of quartic invariants that may or may not be physical. We show that the combination of a geometrical method based on the analysis of the space of invariants, developed by Kim to study symmetry breaking of the Higgs potential, with modern visualization tools provides a resolution to these problems. The approach is applied to the outcome of numerical simulations of particle ordering on a spherical surface and to the ordering of protein shells.
    Language English
    Publishing date 2019-08-20
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.100.012145
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  5. Book ; Online: The propagation of infection fronts in spatially distributed compartment models in epidemiology

    Rudnick, Joseph / Jasnow, David / Vinals, Jorge

    2022  

    Abstract: Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of reaction-diffusion ... ...

    Abstract Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of reaction-diffusion systems, which allow familiar techniques to be applied. The focus is largely on the appearance of soliton-like moving fronts that spread infection to previously uninfected regions. Near threshold dynamical critical behavior and a degree of universality are revealed. Extending two of the models to include a simple nonlinearity in the strength of the binary interaction between a susceptible individual and an infected one, we find the possibility of static coexistence between spatial regions with different levels of infection and an analogy with first-order transitions in thermodynamics.

    Comment: 37 pages, 12 figures
    Keywords Physics - Biological Physics
    Subject code 612
    Publishing date 2022-06-27
    Publishing country us
    Document type Book ; Online
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  6. Article ; Online: Manipulation and amplification of the Casimir force through surface fields using helicity.

    Dantchev, Daniel / Rudnick, Joseph

    Physical review. E

    2017  Volume 95, Issue 4-1, Page(s) 42120

    Abstract: We present both exact and numerical results for the behavior of the Casimir force in O(n) systems with a finite extension L in one direction when the system is subjected to surface fields that induce helicity in the order parameter. We show that for such ...

    Abstract We present both exact and numerical results for the behavior of the Casimir force in O(n) systems with a finite extension L in one direction when the system is subjected to surface fields that induce helicity in the order parameter. We show that for such systems, the Casimir force in certain temperature ranges is of the order of L^{-2}, both above and below the critical temperature, T_{c}, of the bulk system. An example of such a system would be one with chemically modulated bounding surfaces, in which the modulation couples directly to the system's order parameter. We demonstrate that, depending on the parameters of the system, the Casimir force can be either attractive or repulsive. The exact calculations presented are for the one-dimensional XY and Heisenberg models under twisted boundary conditions resulting from finite surface fields that differ in direction by a specified angle, and the three-dimensional Gaussian model with surface fields in the form of plane waves that are shifted in phase with respect to each other. Additionally, we present exact and numerical results for the mean-field version of the three-dimensional O(2) model with finite surface fields on the bounding surfaces. We find that all significant results are consistent with the expectations of finite-size scaling.
    Language English
    Publishing date 2017-04
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.95.042120
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  7. Book ; Online: The Spanning Tree Model for the Assembly Kinetics of RNA Viruses

    Mizrahi, Inbal / Bruinsma, Robijn / Rudnick, Joseph

    2021  

    Abstract: We present a simple kinetic model for the assembly of small single-stranded RNA viruses that can be used to carry out analytical packaging contests between different types of RNA molecules. The RNA selection mechanism is purely kinetic and based on small ...

    Abstract We present a simple kinetic model for the assembly of small single-stranded RNA viruses that can be used to carry out analytical packaging contests between different types of RNA molecules. The RNA selection mechanism is purely kinetic and based on small differences between the assembly energy profiles. RNA molecules that win these packaging contests are characterized by having a minimum "Maximum Ladder Distance" and a maximum "Wrapping Number".The former is a topological invariant that measures the "branchiness" of the genome molecule while the latter measures the ability of the genome molecule to maximally associate with the capsid proteins. The model can also be used study the applicability of the theory of nucleation and growth to viral assembly, which breaks down with increasing strength of the RNA-protein interaction.

    Comment: 18 pages, 25 figures
    Keywords Physics - Biological Physics ; Condensed Matter - Soft Condensed Matter
    Subject code 612
    Publishing date 2021-02-07
    Publishing country us
    Document type Book ; Online
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  8. Book ; Online: The Spanning Tree Model and the Assembly Kinetics of RNA Viruses

    Mizrahi, Inbal / Bruinsma, Robijn / Rudnick, Joseph

    2021  

    Abstract: Single-stranded (ss) RNA viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and the viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization of rather ... ...

    Abstract Single-stranded (ss) RNA viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and the viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization of rather simple models. However, during the self-assembly of complete viral particles in the cytoplasm of an infected cell, the viral genome molecules must be selected from a large pool of very similar host messenger RNA molecules. It is known that the assembly process takes the form of preferential heterogeneous nucleation of capsid proteins on viral RNA molecules ("selective nucleation"). Recently, a simple mathematical model was proposed for the selective nucleation of small ssRNA viruses. In this paper we present a statistical physics analysis of the thermal equilibrium and kinetic properties of that model and show that it can account, at least qualitatively, for numerous observations of the self-assembly of small ssRNA viruses.

    Comment: 19 pages, 26 figures. Submitted to Physical Review E. arXiv admin note: text overlap with arXiv:2102.03941
    Keywords Physics - Biological Physics ; Condensed Matter - Statistical Mechanics
    Subject code 612
    Publishing date 2021-08-11
    Publishing country us
    Document type Book ; Online
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  9. Article: Endocytosis at extremes: Formation and internalization of giant clathrin-coated pits under elevated membrane tension.

    Akatay, Ahmet Ata / Wu, Tianyao / Djakbarova, Umidahan / Thompson, Cristopher / Cocucci, Emanuele / Zandi, Roya / Rudnick, Joseph / Kural, Comert

    Frontiers in molecular biosciences

    2022  Volume 9, Page(s) 959737

    Abstract: Internalization of clathrin-coated vesicles from the plasma membrane constitutes the major endocytic route for receptors and their ligands. Dynamic and structural properties of endocytic clathrin coats are regulated by the mechanical properties of the ... ...

    Abstract Internalization of clathrin-coated vesicles from the plasma membrane constitutes the major endocytic route for receptors and their ligands. Dynamic and structural properties of endocytic clathrin coats are regulated by the mechanical properties of the plasma membrane. Here, we used conventional fluorescence imaging and multiple modes of structured illumination microscopy (SIM) to image formation of endocytic clathrin coats within live cells and tissues of developing fruit fly embryos. High resolution in both spatial and temporal domains allowed us to detect and characterize distinct classes of clathrin-coated structures. Aside from the clathrin pits and plaques detected in distinct embryonic tissues, we report, for the first time, formation of giant coated pits (GCPs) that can be up to two orders of magnitude larger than the canonical pits. In cultured cells, we show that GCP formation is induced by increased membrane tension. GCPs take longer to grow but their mechanism of curvature generation is the same as the canonical pits. We also demonstrate that GCPs split into smaller fragments during internalization. Considering the supporting roles played by actin filament dynamics under mechanically stringent conditions that slow down completion of clathrin coats, we suggest that local changes in the coat curvature driven by actin machinery can drive splitting and internalization of GCPs.
    Language English
    Publishing date 2022-09-21
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2814330-9
    ISSN 2296-889X
    ISSN 2296-889X
    DOI 10.3389/fmolb.2022.959737
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  10. Article ; Online: Kirigami and the Caspar-Klug construction for viral shells with negative Gauss curvature.

    Perotti, Luigi E / Zhang, Kevin / Rudnick, Joseph / Bruinsma, Robijn F

    Physical review. E

    2019  Volume 99, Issue 2-1, Page(s) 22413

    Abstract: In this work we extend the Caspar-Klug construction to the archaeal viruses, which in recent years have captured the attention of many researchers for their ability to thrive in extreme environments. We assume that the shells of archaeal viruses are ... ...

    Abstract In this work we extend the Caspar-Klug construction to the archaeal viruses, which in recent years have captured the attention of many researchers for their ability to thrive in extreme environments. We assume that the shells of archaeal viruses are composed of hexamers and pentamers-as is true for icosahedral viruses-together with heptamers, necessary to introduce negative Gauss curvature. Following the original work of Caspar and Klug, we first construct models capable of reproducing the shape observed in electron microscopy images of archaeal viruses. Next, using the technique of kirigami, we present a systematic way to formulate archaeal virus templates from regular hexagonal lattices. Finally, we utilize the presented techniques to build finite element models of archaeal virus geometries and investigate their shapes as a function of material properties. In particular, using thin-shell elasticity theory, we describe a buckling transition as a function of a modified Föppl-von Kármán number γ^{★} and we show how changes in γ^{★} may initiate the tail formation in the Acidianus two-tailed archaeal virus.
    MeSH term(s) Elasticity ; Models, Molecular ; Normal Distribution ; Viruses/chemistry
    Language English
    Publishing date 2019-04-01
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.99.022413
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