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...

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Main Authors: Jason Peña, Leonardo Dagdug, David Reguera
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/27/3/281
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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.
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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