Projects / Programmes
Orientational Interactions in a Generalized Thomson Problem: Dipole-Stabilized Spherical Nanocontainers
| Code |
Science |
Field |
Subfield |
| 1.02.00 |
Natural sciences and mathematics |
Physics |
|
| Code |
Science |
Field |
| P002 |
Natural sciences and mathematics |
Physics |
| Code |
Science |
Field |
| 1.03 |
Natural Sciences |
Physical sciences |
dipole interaction, finite crystals, self-assembly, orientational order, viral capsids, nanocontainers, Thomson problem
Researchers (9)
Organisations (2)
Abstract
The question of particle arrangements on curved surfaces is, at a first glance, a simple question, which has nonetheless yielded an astounding amount of interesting results, both addressing some of the fundamental questions in physics as well as finding application in numerous systems in soft matter, biophysics, and materials science. In this project proposal, we address an open problem of finding the ground states of particle arrangements on spherical lattices, where the particles interact through anisotropic electrostatic interactions.
Assemblies that take on a (near-)spherical shape are ubiquitous in biophysics and soft matter and take on the form of viral capsids, proteinaceous nanocages, micelles, lipid vesicles, cells, and colloidal structures. In addition to the hard-core repulsion, the interactions between their molecular-to-micron-sized building blocks are largely based on electrostatic interactions of different types. These assemblies are often highly symmetric, and their self-assembly, biological function and biophysical properties are all underpinned by symmetry-breaking transitions.
For the most part, the state-of-the-art studies of assembly on spherical surfaces assume that the interactions between the building blocks are isotropic, resulting in symmetric patterns wherein the building blocks lie on regular lattices. These are most often modelled as Caspar-Klug lattices, solutions of either classical or modified Thomson problem, or maxima of symmetrized spherical harmonics. And while the role of various anisotropic interactions -- and most prominently, dipolar interaction -- has been thoroughly investigated in planar assemblies, this remains an unanswered question in the case of assembly on spheres and other curved surfaces.
We will consider the possibility of stabilizing or destabilizing spherical structures through dipolar interactions, classify the equilibrium states by their symmetry properties, and investigate phase transitions between them. Using numerical minimization with symmetry constraints, we will tackle the problem first for dipoles on fixed lattices with variable orientation order. Later we will extend the possible interactions to include screened, multipolar, van der Waals, and nearest-neighbor interactions, and we will use full positional and orientational minimization to obtain equilibrium states. In this way, we will be able to explore the various possibilities that may arise in different biological systems and under different biochemical conditions in the solvent. We will also construct a theoretical framework to study the effects of thermal fluctuations and external symmetry-breaking effects that may lead to novel ways of controlling assembly and disassembly of spherical nanostructures in biophysics or, on the micron-scale, in colloidal and material science.
The results of this project will benefit various scientific fields. Understanding the ground states of finite, ordered systems in non-trivial topologies is of fundamental importance in the context of hard proteinaceous shells, such as viral capsids, wiffle balls, ferritin cages, carboxysomes or synthetic virus-like particles. The use of specific interactions for the design of self-assembling nanocontainers is an invaluable concept, particularly important for targeted drug delivery. More broadly, the main objectives of the project are also of interest in mathematics, as the fundamental geometric questions related to the Thomson problem and its generalizations remain largely unanswered even on the basic theoretical level. The project will also have an impact beyond its scientific results, establishing new collaborations between two of the leading physics institutions in Slovenia. Lastly, the project will also serve an educational purpose, promoting the modern development of science among the general public and in particular among physics students at various levels, who will be able to join in the activities of the project.
Significance for science
The central question of our proposal is highly relevant, as it addresses at the same time an unanswered problem in theoretical physics—optimal arrangements of dipoles on a spherical surface—and a practical problem of understanding biological assemblies, in particular, viral capsids. Our motivation extends beyond physical virology and is just as well embedded in the general biomedical science and bioengineering, so that the findings of our proposal can lead to follow-up experimental work and, later on, also to practical applications.
When viewed from a purely geometric perspective, the premise of the proposal has a broader relevance for various surface phenomena in physics, exemplified by nanoparticles, vesicles, or shells of anisotropic materials, for macroscopic mechanical applications, and for microfluidic applications. As the electrostatic and magnetic dipoles share the geometry of the interaction, findings can also be applied to studies of molecular magnets, nanoclusters and colloidal magnetic shells. Understanding how dipolar (and other, higher-order multipolar) interactions can be used to stabilize a structure with a given, desired symmetry is an invaluable tool in designing self-assembly procedures that can be implemented for nanocontainers used for drug delivery and other functional colloidal units.
The project will benefit the development of science in Slovenia in several ways. It will strengthen the connection between two of the leading physics institutions in the country, opening a collaboration between researchers with complementary skills, which can continue after completion of the project. The project opens a new line of research, and through presentations of results at international conferences and workshops, it will spark interest of colleagues around the world, opening the possibility of international collaborations, experimental follow-ups, etc. Integrating the knowledge gained from collaboration will further consolidate the position of Slovenian science among the leading experts in the field.
A large part of the researchers involved in the project also teach at the faculty of physics and thus work closely with the students at various stages. Moreover, the researchers working on the project are also involved in popularization of science among the general public. Thus, by providing supervision to students, opportunities to join the activities of the project, and popular science presentations, the project will increase the awareness about the active role of Slovenian researchers in contemporary science.
To sum up, the results of our proposed research should be of immediate interest for a wide ranging scientific audience, and are bound to have a significant impact both in fundamental physics and in bioengineering and physical virology. The research should also have an impact on the level of interest in science among the general public and especially among the students of physics.
Significance for the country
The central question of our proposal is highly relevant, as it addresses at the same time an unanswered problem in theoretical physics—optimal arrangements of dipoles on a spherical surface—and a practical problem of understanding biological assemblies, in particular, viral capsids. Our motivation extends beyond physical virology and is just as well embedded in the general biomedical science and bioengineering, so that the findings of our proposal can lead to follow-up experimental work and, later on, also to practical applications.
When viewed from a purely geometric perspective, the premise of the proposal has a broader relevance for various surface phenomena in physics, exemplified by nanoparticles, vesicles, or shells of anisotropic materials, for macroscopic mechanical applications, and for microfluidic applications. As the electrostatic and magnetic dipoles share the geometry of the interaction, findings can also be applied to studies of molecular magnets, nanoclusters and colloidal magnetic shells. Understanding how dipolar (and other, higher-order multipolar) interactions can be used to stabilize a structure with a given, desired symmetry is an invaluable tool in designing self-assembly procedures that can be implemented for nanocontainers used for drug delivery and other functional colloidal units.
The project will benefit the development of science in Slovenia in several ways. It will strengthen the connection between two of the leading physics institutions in the country, opening a collaboration between researchers with complementary skills, which can continue after completion of the project. The project opens a new line of research, and through presentations of results at international conferences and workshops, it will spark interest of colleagues around the world, opening the possibility of international collaborations, experimental follow-ups, etc. Integrating the knowledge gained from collaboration will further consolidate the position of Slovenian science among the leading experts in the field.
A large part of the researchers involved in the project also teach at the faculty of physics and thus work closely with the students at various stages. Moreover, the researchers working on the project are also involved in popularization of science among the general public. Thus, by providing supervision to students, opportunities to join the activities of the project, and popular science presentations, the project will increase the awareness about the active role of Slovenian researchers in contemporary science.
To sum up, the results of our proposed research should be of immediate interest for a wide ranging scientific audience, and are bound to have a significant impact both in fundamental physics and in bioengineering and physical virology. The research should also have an impact on the level of interest in science among the general public and especially among the students of physics.
Most important scientific results
Interim report
Most important socioeconomically and culturally relevant results
