Kinetic Description of Viral Capsid Self-Assembly Using Mesoscopic Non-Equilibrium Thermodynamics
The self-assembly mechanisms of various complex biological structures, including viral capsids and carboxysomes, have been theoretically studied through numerous kinetic models. However, most of these models focus on the equilibrium aspects of a simplified kinetic description in terms of a single re...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/3/281 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850090800515383296 |
|---|---|
| author | Jason Peña Leonardo Dagdug David Reguera |
| author_facet | Jason Peña Leonardo Dagdug David Reguera |
| author_sort | Jason Peña |
| collection | DOAJ |
| description | The self-assembly mechanisms of various complex biological structures, including viral capsids and carboxysomes, have been theoretically studied through numerous kinetic models. However, most of these models focus on the equilibrium aspects of a simplified kinetic description in terms of a single reaction coordinate, typically the number of proteins in a growing aggregate, which is often insufficient to describe the size and shape of the resulting structure. In this article, we use mesoscopic non-equilibrium thermodynamics (MNET) to derive the equations governing the non-equilibrium kinetics of viral capsid formation. The resulting kinetic equation is a Fokker–Planck equation, which considers viral capsid self-assembly as a diffusive process in the space of the relevant reaction coordinates. We discuss in detail the case of the self-assembly of a spherical (icosahedral) capsid with a fixed radius, which corresponds to a single degree of freedom, and indicate how to extend this approach to the self-assembly of spherical capsids that exhibit radial fluctuations, as well as to tubular structures and systems with higher degrees of freedom. Finally, we indicate how these equations can be solved in terms of the equivalent Langevin equations and be used to determine the rate of formation and size distribution of closed capsids, opening the door to the better understanding and control of the self- assembly process. |
| format | Article |
| id | doaj-art-04f41fd7caa7422d8da64d4c9f152d58 |
| institution | DOAJ |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-04f41fd7caa7422d8da64d4c9f152d582025-08-20T02:42:29ZengMDPI AGEntropy1099-43002025-03-0127328110.3390/e27030281Kinetic Description of Viral Capsid Self-Assembly Using Mesoscopic Non-Equilibrium ThermodynamicsJason Peña0Leonardo Dagdug1David Reguera2Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, Mexico City 09340, MexicoPhysics Department, Universidad Autónoma Metropolitana-Iztapalapa, Mexico City 09340, MexicoDepartament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, SpainThe self-assembly mechanisms of various complex biological structures, including viral capsids and carboxysomes, have been theoretically studied through numerous kinetic models. However, most of these models focus on the equilibrium aspects of a simplified kinetic description in terms of a single reaction coordinate, typically the number of proteins in a growing aggregate, which is often insufficient to describe the size and shape of the resulting structure. In this article, we use mesoscopic non-equilibrium thermodynamics (MNET) to derive the equations governing the non-equilibrium kinetics of viral capsid formation. The resulting kinetic equation is a Fokker–Planck equation, which considers viral capsid self-assembly as a diffusive process in the space of the relevant reaction coordinates. We discuss in detail the case of the self-assembly of a spherical (icosahedral) capsid with a fixed radius, which corresponds to a single degree of freedom, and indicate how to extend this approach to the self-assembly of spherical capsids that exhibit radial fluctuations, as well as to tubular structures and systems with higher degrees of freedom. Finally, we indicate how these equations can be solved in terms of the equivalent Langevin equations and be used to determine the rate of formation and size distribution of closed capsids, opening the door to the better understanding and control of the self- assembly process.https://www.mdpi.com/1099-4300/27/3/281non-equilibrium thermodynamicsentropy productionkinetic equationFokker–Planck equationself-assemblyviral capsid |
| spellingShingle | Jason Peña Leonardo Dagdug David Reguera Kinetic Description of Viral Capsid Self-Assembly Using Mesoscopic Non-Equilibrium Thermodynamics Entropy non-equilibrium thermodynamics entropy production kinetic equation Fokker–Planck equation self-assembly viral capsid |
| title | Kinetic Description of Viral Capsid Self-Assembly Using Mesoscopic Non-Equilibrium Thermodynamics |
| title_full | Kinetic Description of Viral Capsid Self-Assembly Using Mesoscopic Non-Equilibrium Thermodynamics |
| title_fullStr | Kinetic Description of Viral Capsid Self-Assembly Using Mesoscopic Non-Equilibrium Thermodynamics |
| title_full_unstemmed | Kinetic Description of Viral Capsid Self-Assembly Using Mesoscopic Non-Equilibrium Thermodynamics |
| title_short | Kinetic Description of Viral Capsid Self-Assembly Using Mesoscopic Non-Equilibrium Thermodynamics |
| title_sort | kinetic description of viral capsid self assembly using mesoscopic non equilibrium thermodynamics |
| topic | non-equilibrium thermodynamics entropy production kinetic equation Fokker–Planck equation self-assembly viral capsid |
| url | https://www.mdpi.com/1099-4300/27/3/281 |
| work_keys_str_mv | AT jasonpena kineticdescriptionofviralcapsidselfassemblyusingmesoscopicnonequilibriumthermodynamics AT leonardodagdug kineticdescriptionofviralcapsidselfassemblyusingmesoscopicnonequilibriumthermodynamics AT davidreguera kineticdescriptionofviralcapsidselfassemblyusingmesoscopicnonequilibriumthermodynamics |