1
|
Tajana M, Trovato A, Tiana G. Key interaction patterns in proteins revealed by cluster expansion of the partition function. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:95. [PMID: 36447074 DOI: 10.1140/epje/s10189-022-00250-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Accepted: 11/19/2022] [Indexed: 06/16/2023]
Abstract
The native conformation of structured proteins is stabilized by a complex network of interactions. We analyzed the elementary patterns that constitute such network and ranked them according to their importance in shaping protein sequence design. To achieve this goal, we employed a cluster expansion of the partition function in the space of sequences and evaluated numerically the statistical importance of each cluster. An important feature of this procedure is that it is applied to a dense finite system. We found that patterns that contribute most to the partition function are cycles with even numbers of nodes, while cliques are typically detrimental. Each cluster also gives a contribute to the sequence entropy, which is a measure of the evolutionary designability of a fold. We compared the entropies associated with different interaction patterns to their abundances in the native structures of real proteins.
Collapse
Affiliation(s)
- Matteo Tajana
- Department of Physics, Università degli Studi di Milano, Via Celoria 16, 20133, Milan, Italy
| | - Antonio Trovato
- Department of Physics and Astronomy "G. Galilei", Università degli Studi di Padova and INFN, Via Marzolo 8, 35121, Padova, Italy
| | - Guido Tiana
- Department of Physics and Center for Complexity and Biosystems, Università degli Studi di Milano and INFN, Via Celoria 16, 20133, Milan, Italy.
| |
Collapse
|
2
|
Di Cairano L, Capelli R, Bel-Hadj-Aissa G, Pettini M. Topological origin of the protein folding transition. Phys Rev E 2022; 106:054134. [PMID: 36559453 DOI: 10.1103/physreve.106.054134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Accepted: 10/19/2022] [Indexed: 06/17/2023]
Abstract
In this paper, a geometrical and thermodynamical analysis of the global properties of the potential energy landscape of a minimalistic model of a polypeptide is presented. The global geometry of the potential energy landscape is supposed to contain relevant information about the properties of a given sequence of amino acids, that is, to discriminate between a random heteropolymer and a protein. By considering the SH3 and PYP protein-sequences and their randomized versions it turns out that, in addition to the standard signatures of the folding transition-discriminating between protein sequences of amino acids and random heteropolymer sequences-also peculiar geometric signatures of the equipotential hypersurfaces in configuration space can discriminate between proteins and random heteropolymers. Interestingly, these geometric signatures are the "shadows" of deeper topological changes that take place in correspondence with the protein folding transition. The protein folding transition takes place in systems with a small number of degrees of freedom (very far from the Avogadro number) and in the absence of a symmetry-breaking phenomenon. Nevertheless, seen from the deepest level of topology changes of equipotential submanifolds of phase space, the protein folding transition fully qualifies as a phase transition.
Collapse
Affiliation(s)
- Loris Di Cairano
- Computational Biomedicine, Institute for Advanced Simulation IAS-5, and Institute of Neuroscience and Medicine INM-9, Forschungszentrum Jülich, 52425 Jülich, Germany
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Riccardo Capelli
- Department of Biosciences, Università degli Studi di Milano, Via Celoria 26, 20133 Milano, Italy
| | - Ghofrane Bel-Hadj-Aissa
- University of Siena, Via Roma 56, 53100 Siena, Italy
- Aix-Marseille Univ, Université de Toulon, CNRS, France
- Centre de Physique Théorique, UMR 7332, Marseille, France
| | - Marco Pettini
- Aix-Marseille Univ, Université de Toulon, CNRS, France
- Centre de Physique Théorique, UMR 7332, Marseille, France
| |
Collapse
|
3
|
Negri M, Tiana G, Zecchina R. Native state of natural proteins optimizes local entropy. Phys Rev E 2021; 104:064117. [PMID: 35030941 DOI: 10.1103/physreve.104.064117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 11/24/2021] [Indexed: 06/14/2023]
Abstract
The differing ability of polypeptide conformations to act as the native state of proteins has long been rationalized in terms of differing kinetic accessibility or thermodynamic stability. Building on the successful applications of physical concepts and sampling algorithms recently introduced in the study of disordered systems, in particular artificial neural networks, we quantitatively explore how well a quantity known as the local entropy describes the native state of model proteins. In lattice models and all-atom representations of proteins, we are able to efficiently sample high local entropy states and to provide a proof of concept of enhanced stability and folding rate. Our methods are based on simple and general statistical-mechanics arguments, and thus we expect that they are of very general use.
Collapse
Affiliation(s)
- M Negri
- Department Applied Science and Technology, Politecnico di Torino, CorsoDuca degli Abruzzi 24, I-10129 Turin, Italy
| | - G Tiana
- Department of Physics and Center for Complexity and Biosystems, Università degli Studi di Milano and INFN, via Celoria 16, 20133 Milan, Italy
| | - R Zecchina
- Artificial Intelligence Lab, Bocconi University, Via Sarfatti, 25, 20136 Milan, Italy
| |
Collapse
|
4
|
Negri M, Gherardi M, Tiana G, Cosentino Lagomarsino M. Spontaneous domain formation in disordered copolymers as a mechanism for chromosome structuring. SOFT MATTER 2018; 14:6128-6136. [PMID: 29998272 DOI: 10.1039/c8sm00468d] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Motivated by the problem of domain formation in chromosomes, we studied a co-polymer model where only a subset of the monomers feel attractive interactions. These monomers are displaced randomly from a regularly-spaced pattern, thus introducing some quenched disorder in the system. Previous work has shown that in the case of regularly-spaced interacting monomers this chain can fold into structures characterized by multiple distinct domains of consecutive segments. In each domain, attractive interactions are balanced by the entropy cost of forming loops. We show by advanced replica-exchange simulations that adding disorder in the position of the interacting monomers further stabilizes these domains. The model suggests that the partitioning of the chain into well-defined domains of consecutive monomers is a spontaneous property of heteropolymers. In the case of chromosomes, evolution could have acted on the spacing of interacting monomers to modulate in a simple way the underlying domains for functional reasons.
Collapse
Affiliation(s)
- Matteo Negri
- Department of Physics, Universitá degli Studi di Milano, via Celoria 16, 20133 Milano, Italy.
| | | | | | | |
Collapse
|
5
|
Zhan Y, Giorgetti L, Tiana G. Looping probability of random heteropolymers helps to understand the scaling properties of biopolymers. Phys Rev E 2016; 94:032402. [PMID: 27739813 DOI: 10.1103/physreve.94.032402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2016] [Indexed: 06/06/2023]
Abstract
Random heteropolymers are a minimal description of biopolymers and can provide a theoretical framework to the investigate the formation of loops in biophysical experiments. The looping probability as a function of polymer length was observed to display in some biopolymers, like chromosomes in cell nuclei or long RNA chains, anomalous scaling exponents. Combining a two-state model with self-adjusting simulated-tempering calculations, we calculate numerically the looping properties of several realizations of the random interactions within the chain. We find a continuous set of exponents upon varying the temperature, which arises from finite-size effects and is amplified by the disorder of the interactions. We suggest that this could provide a simple explanation for the anomalous scaling exponents found in experiments. In addition, our results have important implications notably for the study of chromosome folding as they show that scaling exponents cannot be the sole criteria for testing hypothesis-driven models of chromosome architecture.
Collapse
Affiliation(s)
- Y Zhan
- Friedrich Miescher Institute for Biomedical Research, Maulbeerstrasse 66, CH-4058 Basel, Switzerland
| | - L Giorgetti
- Friedrich Miescher Institute for Biomedical Research, Maulbeerstrasse 66, CH-4058 Basel, Switzerland
| | - G Tiana
- Center for Complexity and Biosystems and Department of Physics, Università degli Studi di Milano and INFN, via Celoria 16, 20133 Milano, Italy
| |
Collapse
|
6
|
Detecting selection on protein stability through statistical mechanical models of folding and evolution. Biomolecules 2014; 4:291-314. [PMID: 24970217 PMCID: PMC4030984 DOI: 10.3390/biom4010291] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2013] [Revised: 02/13/2014] [Accepted: 02/14/2014] [Indexed: 12/31/2022] Open
Abstract
The properties of biomolecules depend both on physics and on the evolutionary process that formed them. These two points of view produce a powerful synergism. Physics sets the stage and the constraints that molecular evolution has to obey, and evolutionary theory helps in rationalizing the physical properties of biomolecules, including protein folding thermodynamics. To complete the parallelism, protein thermodynamics is founded on the statistical mechanics in the space of protein structures, and molecular evolution can be viewed as statistical mechanics in the space of protein sequences. In this review, we will integrate both points of view, applying them to detecting selection on the stability of the folded state of proteins. We will start discussing positive design, which strengthens the stability of the folded against the unfolded state of proteins. Positive design justifies why statistical potentials for protein folding can be obtained from the frequencies of structural motifs. Stability against unfolding is easier to achieve for longer proteins. On the contrary, negative design, which consists in destabilizing frequently formed misfolded conformations, is more difficult to achieve for longer proteins. The folding rate can be enhanced by strengthening short-range native interactions, but this requirement contrasts with negative design, and evolution has to trade-off between them. Finally, selection can accelerate functional movements by favoring low frequency normal modes of the dynamics of the native state that strongly correlate with the functional conformation change.
Collapse
|
7
|
D'Amico M, Di Carlo MG, Groenning M, Militello V, Vetri V, Leone M. Thioflavin T Promotes Aβ(1-40) Amyloid Fibrils Formation. J Phys Chem Lett 2012; 3:1596-601. [PMID: 26285714 DOI: 10.1021/jz300412v] [Citation(s) in RCA: 72] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Fibrillogenesis of the small peptide Aβ(1-40) is considered to be the hallmark of Alzheimer's disease. Some evidence indicates small oligomers, rather than mature fibrils, as the key cytotoxic agents. The fluorescent dye Thioflavin T (ThT) is often used to detect amyloid deposits in both in vivo and in vitro experiments, and it is used to study kinetic measurements, under the fundamental hypothesis that this probe does not influence the aggregation processes. We report experimental data showing that ThT may promote the Aβ(1-40) peptide amyloid aggregation changing solvent-peptide interactions and stabilizing more ordered β-like conformation. This finding has a two-fold importance: It is a fundamental warning in all fibrillation experiments where ThT is used as fluorescent probe, and it suggests that ThT, accelerating fibril formation, could be used to reduce the presence of transient small oligomers, thus interfering with the pathogenic impact of Aβ peptide.
Collapse
Affiliation(s)
- Michele D'Amico
- †Dip. di Fisica, Università degli Studi di Palermo, Via Archirafi 36, I-90123, Palermo, Italy
| | - Maria Giovanna Di Carlo
- †Dip. di Fisica, Università degli Studi di Palermo, Via Archirafi 36, I-90123, Palermo, Italy
| | - Minna Groenning
- ‡Department of Pharmacy, Faculty of Health and Medical Sciences, University of Copenhagen, Universitetsparken 2, DK-2100 Copenhagen, Denmark
| | - Valeria Militello
- †Dip. di Fisica, Università degli Studi di Palermo, Via Archirafi 36, I-90123, Palermo, Italy
| | - Valeria Vetri
- †Dip. di Fisica, Università degli Studi di Palermo, Via Archirafi 36, I-90123, Palermo, Italy
| | - Maurizio Leone
- †Dip. di Fisica, Università degli Studi di Palermo, Via Archirafi 36, I-90123, Palermo, Italy
| |
Collapse
|
8
|
Bastolla U, Bruscolini P, Velasco JL. Sequence determinants of protein folding rates: Positive correlation between contact energy and contact range indicates selection for fast folding. Proteins 2012; 80:2287-304. [DOI: 10.1002/prot.24118] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2011] [Revised: 05/14/2012] [Accepted: 05/17/2012] [Indexed: 11/12/2022]
|