Energy Landscapes, Self‐Assembly and Viruses

D J Wales

doi:10.1080/10273660500149570

Abstract

Phenomena such as protein folding, crystallisation, self‐assembly, and the observation of magic number clusters in molecular beams are all the result of non‐random searches. Analysis of the underlying potential energy surface may provide a unifying framework to explain how such events occur as the result of a guided exploration of the landscape. In particular, icosahedral shells composed of 12 pentagonal pyramids are found to be thermodynamically favourable and kinetically accessible when the pyramids are not too spiky and not too flat. Hence, viruses with icosahedral capsids not only minimise the genetic material required to encode the repeated subunits, but may also utilise the favourable properties of a potential energy surface that effectively directs self‐assembly.

Highlights

The structure, dynamics and thermodynamics of any molecular system are determined at a fundamental level by the interatomic or intermolecular forces
For the model based upon pentagonal pyramids it is the height of the disks, h, which primarily determines the optimal hinge angle for a pair of pentamers, and the curvature is close to the optimal value for icosahedral packing when h 1⁄4 r=2 [9]
The corresponding graph corresponds to the “palm tree” form identified in previous work [23]. This pattern is characteristic of systems for which efficient relaxation to the global minimum occurs over a wide range of temperature, such as magic number clusters observed in molecular beam studies

Summary

Introduction

The structure, dynamics and thermodynamics of any molecular system are determined at a fundamental level by the interatomic or intermolecular forces. The interplay of these forces governs the form of the potential energy surface (PES), including the geometries of the local minima, their distribution in energy and the magnitude of the barriers that separate them. The underlying PES was found to possess all the characteristics necessary for efficient relaxation to an icosahedral arrangement, providing the constituent pentagonal pyramids exhibit an appropriate morphology.

Results

Conclusion