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Škrbić T, Giacometti A, Hoang TX, Maritan A, Banavar JR. A Tale of Two Chains: Geometries of a Chain Model and Protein Native State Structures. Polymers (Basel) 2024; 16:502. [PMID: 38399880 PMCID: PMC10892082 DOI: 10.3390/polym16040502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Revised: 02/06/2024] [Accepted: 02/10/2024] [Indexed: 02/25/2024] Open
Abstract
Linear chain molecules play a central role in polymer physics with innumerable industrial applications. They are also ubiquitous constituents of living cells. Here, we highlight the similarities and differences between two distinct ways of viewing a linear chain. We do this, on the one hand, through the lens of simulations for a standard polymer chain of tethered spheres at low and high temperatures and, on the other hand, through published experimental data on an important class of biopolymers, proteins. We present detailed analyses of their local and non-local structures as well as the maps of their closest contacts. We seek to reconcile the startlingly different behaviors of the two types of chains based on symmetry considerations.
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Affiliation(s)
- Tatjana Škrbić
- Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, 30170 Venice, Italy;
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, OR 97403, USA;
| | - Achille Giacometti
- Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, 30170 Venice, Italy;
- European Centre for Living Technology (ECLT), Ca’ Bottacin, Dorsoduro 3911, Calle Crosera, 30123 Venice, Italy
| | - Trinh X. Hoang
- Institute of Physics, Vietnam Academy of Science and Technology, Hanoi 11108, Vietnam;
| | - Amos Maritan
- Department of Physics and Astronomy, University of Padua, 35122 Padua, Italy;
| | - Jayanth R. Banavar
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, OR 97403, USA;
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Marcato D, Giacometti A, Maritan A, Rosa A. Phase behaviour of semiflexible lattice polymers in poor-solvent solution: Mean-field theory and Monte Carlo simulations. J Chem Phys 2023; 159:154901. [PMID: 37843062 DOI: 10.1063/5.0171911] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 09/22/2023] [Indexed: 10/17/2023] Open
Abstract
We study a solution of interacting semiflexible polymers with curvature energy in poor-solvent conditions on the d-dimensional cubic lattice using mean-field theory and Monte Carlo computer simulations. Building upon past studies on a single chain, we construct a field-theory representation of the system and solve it within a mean-field approximation supported by Monte Carlo simulations in d = 3. A gas-liquid transition is found in the temperature-density plane that is then interpreted in terms of real systems. Interestingly, we find this transition to be independent of the bending rigidity. Past classical Flory-Huggins and Flory mean-field results are shown to be particular cases of this more general framework. Perspectives in terms of guiding experimental results towards optimal conditions are also proposed.
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Affiliation(s)
- Davide Marcato
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari Venezia, 30123 Venezia, Italy
- European Centre for Living Technology (ECLT) Ca' Bottacin, 3911 Dorsoduro Calle Crosera, 30123 Venezia, Italy
| | - Amos Maritan
- Laboratory of Interdisciplinary Physics, Department of Physics and Astronomy "G. Galilei," University of Padova, Padova, Italy and INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - Angelo Rosa
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
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Škrbić T, Hoang TX, Giacometti A, Maritan A, Banavar JR. Marginally compact phase and ordered ground states in a model polymer with side spheres. Phys Rev E 2021; 104:L012501. [PMID: 34412214 DOI: 10.1103/physreve.104.l012501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2021] [Accepted: 06/14/2021] [Indexed: 11/07/2022]
Abstract
We present the results of a quantitative study of the phase behavior of a model polymer chain with side spheres using two independent computer simulation techniques. We find that the mere addition of side spheres results in key modifications of standard polymer behavior. One obtains a marginally compact phase at low temperatures; the structures in this phase are reduced in dimensionality and are ordered, they include strands assembled into sheets and a variety of helices, and at least one of the transitions on lowering the temperature to access these ordered states is found to be first order. Our model serves to partially bridge conventional polymer phases with biomolecular phases.
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Affiliation(s)
- Tatjana Škrbić
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA and Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Campus Scientifico, Edificio Alfa, Via Torino 155, 30170 Venezia Mestre, Italy
| | - Trinh Xuan Hoang
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi 11108, Vietnam
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Campus Scientifico, Edificio Alfa, Via Torino 155, 30170 Venezia Mestre, Italy and European Center for Living Technologies, Ca' Bottacin, Dorsoduro 3911, Calle Crosera, 30123 Venezia, Italy
| | - Amos Maritan
- Dipartimento di Fisica e Astronomia, Università di Padova and INFN, Via Marzolo 8, 35131 Padova, Italy
| | - Jayanth R Banavar
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA
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Škrbić T, Hoang TX, Giacometti A, Maritan A, Banavar JR. Spontaneous dimensional reduction and ground state degeneracy in a simple chain model. Phys Rev E 2021; 104:L012101. [PMID: 34412247 DOI: 10.1103/physreve.104.l012101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Accepted: 04/08/2021] [Indexed: 11/07/2022]
Abstract
Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first-order transition from a high-temperature random coil phase to a highly unusual low-temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures [we call these PoSSuM (Planar Structures with Secondary Motifs)] in the phase and protein native state structures.
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Affiliation(s)
- Tatjana Škrbić
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA and Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy
| | - Trinh Xuan Hoang
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi 11108, Vietnam
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy and European Center for Living Technologies (ECLT), Ca' Bottacin, Dorsoduro 3911 Calle Crosera, 30123 Venezia, Italy
| | - Amos Maritan
- Dipartimento di Fisica e Astronomia, Università di Padova and INFN, via Marzolo 8, 35131 Padova, Italy
| | - Jayanth R Banavar
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA
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Wicks TJ, Wattis JAD, Graham RS. Monte–Carlo simulation of crystallization in single‐chain square‐well homopolymers. POLYMER CRYSTALLIZATION 2021. [DOI: 10.1002/pcr2.10146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Thomas J. Wicks
- School of Mathematical Sciences University of Nottingham Nottingham UK
| | | | - Richard S. Graham
- School of Mathematical Sciences University of Nottingham Nottingham UK
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Mitra D, Chatterji A. Transient helix formation in charged semiflexible polymers without confinement effects. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 33:044001. [PMID: 32987379 DOI: 10.1088/1361-648x/abbc32] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2020] [Accepted: 09/28/2020] [Indexed: 06/11/2023]
Abstract
Switching on generic interactions e.g. the Coulomb potential or other long ranged spherically symmetric repulsive interactions between monomers of bead-spring model of a semi-flexible polymer induce instabilities in a semiflexible polymer chain to form transient helical structures. Our proposed mechanism could explain the spontaneous emergence of helical order in stiff (bio-) polymers as a chain gets charged from a neutral state. But since the obtained helical structures dissolve away with time, hydrogen bonding (or other additional mechanisms), would be required to form stabilized helical structures as observed in nature (such as in biological macro-molecules). The emergence of the helix is independent of the molecular details of the monomer constituent. The key factors which control the emergence of the helical structure is the persistence length and the charge density. We have avoided using torsional potentials to obtain the transient helical structures. Moreover, we can drive the semiflexible polymer to form helices in a recurring manner by periodically increasing and decreasing the effective charge of the monomers. If the two polymer ends are tethered to two surfaces separated by a distance equal to the contour length of the polymeric chain, which could be in the range 10 nm-μ, the life time of the helical structures formed is increased.
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Affiliation(s)
- Debarshi Mitra
- Department of Physics, IISER-Pune, Dr Homi Bhaba Road, Pune-411008, India
| | - Apratim Chatterji
- Department of Physics, IISER-Pune, Dr Homi Bhaba Road, Pune-411008, India
- Center for Energy Science, IISER-Pune, Dr Homi Bhaba Road, Pune-411008, India
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