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Škrbić T, Giacometti A, Hoang TX, Maritan A, Banavar JR. Amino-Acid Characteristics in Protein Native State Structures. Biomolecules 2024; 14:805. [PMID: 39062519 PMCID: PMC11274641 DOI: 10.3390/biom14070805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2024] [Revised: 07/02/2024] [Accepted: 07/05/2024] [Indexed: 07/28/2024] Open
Abstract
The molecular machines of life, proteins, are made up of twenty kinds of amino acids, each with distinctive side chains. We present a geometrical analysis of the protrusion statistics of side chains in more than 4000 high-resolution protein structures. We employ a coarse-grained representation of the protein backbone viewed as a linear chain of Cα atoms and consider just the heavy atoms of the side chains. We study the large variety of behaviors of the amino acids based on both rudimentary structural chemistry as well as geometry. Our geometrical analysis uses a backbone Frenet coordinate system for the common study of all amino acids. Our analysis underscores the richness of the repertoire of amino acids that is available to nature to design protein sequences that fit within the putative native state folds.
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Affiliation(s)
- Tatjana Škrbić
- Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, Campus Scientifico, Via Torino 155, 30170 Venice Mestre, 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, Campus Scientifico, Via Torino 155, 30170 Venice Mestre, 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, 10 DaoTan, Ba Dinh, Hanoi 11108, Vietnam;
| | - Amos Maritan
- Department of Physics and Astronomy, University of Padua, Via Marzolo 8, 35131 Padua, Italy;
| | - Jayanth R. Banavar
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, OR 97403, USA;
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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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Banavar JR, Giacometti A, Hoang TX, Maritan A, Škrbić T. A geometrical framework for thinking about proteins. Proteins 2023. [PMID: 37565735 DOI: 10.1002/prot.26567] [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: 06/24/2023] [Revised: 07/16/2023] [Accepted: 07/21/2023] [Indexed: 08/12/2023]
Abstract
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We employ analytic calculations and detailed Monte Carlo simulations to explore some consequences of our theory. The predictions of our approach are in accord with experimental data. Our framework provides a rationalization for understanding the common characteristics of proteins. Our results show that the free energy landscape of a globular protein is pre-sculpted at the backbone level, sequences and functionalities evolve in the fixed backdrop of the folds determined by geometry and symmetry, and that protein structures are unique in being simultaneously characterized by stability, diversity, and sensitivity.
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Affiliation(s)
- Jayanth R Banavar
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon, USA
| | - Achille Giacometti
- Ca' Foscari University of Venice, Department of Molecular Sciences and Nanosystems, Venice, Italy
- European Centre for Living Technology (ECLT), Venice, Italy
| | - Trinh X Hoang
- Vietnam Academy of Science and Technology, Institute of Physics, Hanoi, Vietnam
| | - Amos Maritan
- University of Padua, Department of Physics and Astronomy, Padua, Italy
| | - Tatjana Škrbić
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon, USA
- Ca' Foscari University of Venice, Department of Molecular Sciences and Nanosystems, Venice, 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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Škrbić T, Banavar JR, Giacometti A. Chain stiffness bridges conventional polymer and bio-molecular phases. J Chem Phys 2019; 151:174901. [PMID: 31703491 DOI: 10.1063/1.5123720] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses-one yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations, including a coil, a globule, a toroid, rods, helices, and zig-zag strands resembling β-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffnesses play different physical roles and have very distinct effects on the nature of the ground state of the conformation of a chain, even if they lead to identical persistence lengths.
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Affiliation(s)
- Tatjana Škrbić
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, Oregon 97403-1274, USA
| | - Jayanth R Banavar
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, Oregon 97403-1274, USA
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy
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Škrbić T, Hoang TX, Maritan A, Banavar JR, Giacometti A. Local symmetry determines the phases of linear chains: a simple model for the self-assembly of peptides. SOFT MATTER 2019; 15:5596-5613. [PMID: 31259346 DOI: 10.1039/c9sm00851a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We discuss the relation between the emergence of new phases with broken symmetry within the framework of simple models of biopolymers. We start with a classic model for a chain molecule of spherical beads tethered together, with the steric constraint that non-consecutive beads cannot overlap, and with a pairwise attractive square well potential accounting for the hydrophobic effect and promoting compaction. We then discuss the consequences of the successive breaking of spurious symmetries. First, we allow the partial interpenetration of consecutive beads. In addition to the standard high temperature coil phase and the low temperature collapsed phase, this results in a new class of marginally compact ground states comprising conformations reminiscent of α-helices and β-sheets, the building blocks of the native states of globular proteins. We then discuss the effect of a further symmetry breaking of the cylindrical symmetry on attaching a side-sphere to the backbone beads along the negative normal of the chain, to mimic the presence of side chains in real proteins. This leads to the emergence of a novel phase within the previously obtained marginally compact phase, with the appearance of more complex secondary structure assemblies. The potential importance of this new phase in the de novo design of self-assembled peptides is highlighted.
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Affiliation(s)
- Tatjana Škrbić
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, OR 97403-1274, 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
- Center for Computational Physics Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan St., Hanoi, Vietnam.
| | - Amos Maritan
- Dipartimento di Fisica e Astronomia, Università di Padova, and INFN, via Marzolo 8, I-35131 Padova, Italy.
| | - Jayanth R Banavar
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, OR 97403-1274, USA.
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy.
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Gadiyaram V, Vishveshwara S, Vishveshwara S. From Quantum Chemistry to Networks in Biology: A Graph Spectral Approach to Protein Structure Analyses. J Chem Inf Model 2019; 59:1715-1727. [DOI: 10.1021/acs.jcim.9b00002] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Vasundhara Gadiyaram
- IISc Mathematics Initiative (IMI), Indian Institute of Science, C V Raman Road, Bengaluru, Karnataka 560012, India
| | - Smitha Vishveshwara
- Department of Physics, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801-3080, United States
| | - Saraswathi Vishveshwara
- Molecular Biophysics Unit, Indian Institute of Science, C V Raman Road, Bengaluru, Karnataka 560012, India
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