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Symmetry
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Emergent Order Parameters in Complex Biophysical Systems
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Emergent Order Parameters in Complex Biophysical Systems

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Life Sciences".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 21282

Special Issue Editors

Prof. Dr. Theo Odijk

E-Mail Website
Guest Editor
Lorentz Institute for Theoretical Physics, Leiden University, Leiden, The Netherlands
Interests: exact sciences
Prof. Dr. Paul van der Schoot

E-Mail Website
Guest Editor
Theory of Polymers and Soft Matter, Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
Interests: soft matter

Special Issue Information

Dear Colleagues,

In theoretical physics, the introduction of order parameters is well known to be subtle. The breaking of symmetry in a physical system is connected with some order parameter, though the definition of the latter is often vague. For instance, in the case of the isotropic–nematic transition, the order parameter is often chosen to be the average of the second Legendre polynomial. However, the nematic is more often than not so highly ordered that the orientational distribution is asymptotically Gaussian. When we do not understand the physical properties of a system (e.g., high temperature supercomductors), we do not know the correct order parameter(s).  

In the case of biophysical and biological systems, we are still in virgin territory with regard to the introduction of the appropriate order parameters. Theoretical physics has mechanics as its foundation. The generalized coordinates and momenta are the canonical variables of choice. In biology, the genescould be one set of variables imposing restrictions on coarse-grained parameters, but this connection is totally obscure at present. 

The objective of this Special Issue is to bring together theoretical and experimental investigations seeking to find new “order parameters” in biology and biophysics.

Prof. Dr. Theo Odijk
Prof. Dr. Paul van der Schoot
Guest Editors

Manuscript Submission Information

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Keywords

  • Pattern formation
  • Protein networks
  • Chromatin
  • Nucleoid
  • Mathematical biology
  • DNA segregation
  • Mitosis
  • Viscoelastic cytoplasm
  • Virus dynamics
  • Evolutionary dynamics
  • Cellular interactions
  • Organ tissue formation
  • Microtubular dynamics
  • Bacterial colonies
  • Supercoiling dynamics
  • Protein folding

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Published Papers (7 papers)

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Research

12 pages, 421 KiB  
Article
How a Nonequilibrium Bath and a Potential Well Lead to Broken Time-Reversal Symmetry—First-Order Corrections on Fluctuation–Dissipation Relations
by Steven Yuvan, Nick Bellardini and Martin Bier
Symmetry 2022, 14(5), 1042; https://doi.org/10.3390/sym14051042 - 19 May 2022
Cited by 2 | Viewed by 2013
Abstract
The noise that is associated with nonequilibrium processes commonly features more outliers and is therefore often taken to be Lévy noise. For a Langevin particle that is subjected to Lévy noise, the kicksizes are drawn not from a Gaussian distribution, but from an [...] Read more.
The noise that is associated with nonequilibrium processes commonly features more outliers and is therefore often taken to be Lévy noise. For a Langevin particle that is subjected to Lévy noise, the kicksizes are drawn not from a Gaussian distribution, but from an α-stable distribution. For a Gaussian-noise-subjected particle in a potential well, microscopic reversibility applies. However, it appears that the time-reversal-symmetry is broken for a Lévy-noise-subjected particle in a potential well. Major obstacles in the analysis of Langevin equations with Lévy noise are the lack of simple analytic formulae and the infinite variance of the α-stable distribution. We propose a measure for the violation of time-reversal symmetry, and we present a procedure in which this measure is central to a controlled imposing of time-reversal asymmetry. The procedure leads to behavior that mimics much of the effects of Lévy noise. Our imposing of such nonequilibrium leads to concise analytic formulae and does not yield any divergent variances. Most importantly, the theory leads to simple corrections on the Fluctuation–Dissipation Relation. Full article
(This article belongs to the Special Issue Emergent Order Parameters in Complex Biophysical Systems)
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15 pages, 287 KiB  
Article
Foundations of Biology
by Jean-Louis Sikorav, Alan Braslau and Arach Goldar
Symmetry 2021, 13(9), 1701; https://doi.org/10.3390/sym13091701 - 15 Sep 2021
Viewed by 2803
Abstract
It is often stated that there are no laws in biology, where everything is contingent and could have been otherwise, being solely the result of historical accidents. Furthermore, the customary introduction of fundamental biological entities such as individual organisms, cells, genes, catalysts, and [...] Read more.
It is often stated that there are no laws in biology, where everything is contingent and could have been otherwise, being solely the result of historical accidents. Furthermore, the customary introduction of fundamental biological entities such as individual organisms, cells, genes, catalysts, and motors remains largely descriptive; constructive approaches involving deductive reasoning appear, in comparison, almost absent. As a consequence, both the logical content and principles of biology need to be reconsidered. The present article describes an inquiry into the foundations of biology. The foundations of biology are built in terms of elements, logic, and principles, using both the language and the general methods employed in other disciplines. This approach assumes the existence of a certain unity of human knowledge that transcends discipline boundaries. Leibniz’s principle of sufficient reason is revised through a study of the complementary concepts of symmetry and asymmetry and of necessity and contingency. This is used to explain how these concepts are involved in the elaboration of theories or laws of nature. Four fundamental theories of biology are then identified: cell theory, Darwin’s theory of natural selection, an informational theory of life (which includes Mendel’s theory of inheritance) and a physico-chemical theory of life. Atomism and deductive reasoning are shown to enter into the elaboration of the concepts of natural selection, individual living organisms, cells, and their reproduction, genes, as well as catalysts and motors. This work contributes to clarify the philosophical and logical structure of biology and its major theories. This should ultimately lead to a better understanding of the origin of life, of system and synthetic biology, and of artificial life. Full article
(This article belongs to the Special Issue Emergent Order Parameters in Complex Biophysical Systems)
12 pages, 2366 KiB  
Article
On the Emergence of Orientational Order in Folded Proteins with Implications for Allostery
by Debayan Chakraborty, Mauro Lorenzo Mugnai and D. Thirumalai
Symmetry 2021, 13(5), 770; https://doi.org/10.3390/sym13050770 - 29 Apr 2021
Cited by 4 | Viewed by 2858
Abstract
The beautiful structures of single- and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein structures are considered to be aperiodic, and may [...] Read more.
The beautiful structures of single- and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein structures are considered to be aperiodic, and may have evolved this way for functional purposes, especially in instances that require a combination of softness and rigidity within the same molecule. By analyzing the solved protein structures, we show that orientational symmetry is broken in the aperiodic arrangement of the secondary structure elements (SSEs), which we deduce by calculating the nematic order parameter, P2. We find that the folded structures are nematic droplets with a broad distribution of P2. We argue that a non-zero value of P2, leads to an arrangement of the SSEs that can resist external forces, which is a requirement for allosteric proteins. Such proteins, which resist mechanical forces in some regions while being flexible in others, transmit signals from one region of the protein to another (action at a distance) in response to binding of ligands (oxygen, ATP, or other small molecules). Full article
(This article belongs to the Special Issue Emergent Order Parameters in Complex Biophysical Systems)
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17 pages, 958 KiB  
Article
Theory of Inhomogeneous Rod-like Coulomb Fluids
by Rudolf Podgornik
Symmetry 2021, 13(2), 274; https://doi.org/10.3390/sym13020274 - 5 Feb 2021
Cited by 4 | Viewed by 2228
Abstract
A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact via long range Coulomb and short range nematic interactions. The field theory is then solved on a [...] Read more.
A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact via long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson–Boltzmann and Maier–Saupe equations. Explicit solutions are finally obtained for a rod-like counterion-only system in proximity to a charged planar wall. The nematic order parameter profile, the counterion density profile and the electrostatic potential profile are interpreted within the framework of a nematic–isotropic wetting phase with a Donnan potential difference. Full article
(This article belongs to the Special Issue Emergent Order Parameters in Complex Biophysical Systems)
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10 pages, 2216 KiB  
Article
Bootstrapped Motion of an Agent on an Adaptive Resource Landscape
by Trung V. Phan, Gao Wang, Liyu Liu and Robert H. Austin
Symmetry 2021, 13(2), 225; https://doi.org/10.3390/sym13020225 - 29 Jan 2021
Cited by 7 | Viewed by 2665
Abstract
We theoretically show that isolated agents that locally and symmetrically consume resources and sense positive resource gradients can generate constant motion via bootstrapped resource gradients in the absence of any externally imposed gradients, and we show a realization of this motion using robots. [...] Read more.
We theoretically show that isolated agents that locally and symmetrically consume resources and sense positive resource gradients can generate constant motion via bootstrapped resource gradients in the absence of any externally imposed gradients, and we show a realization of this motion using robots. This self-generated agent motion can be coupled with neighboring agents to act as a spontaneously broken symmetry seed for emergent collective dynamics. We also show that in a sufficiently weak externally imposed gradient, it is possible for an agent to move against an external resource gradient due to the local resource depression on the landscape created by an agent. This counter-intuitive boot-strapped motion against an external gradient is demonstrated with a simple robot system on an light-emitting diode (LED) light-board. Full article
(This article belongs to the Special Issue Emergent Order Parameters in Complex Biophysical Systems)
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13 pages, 743 KiB  
Article
Complete Quantum Information in the DNA Genetic Code
by Michel Planat, Raymond Aschheim, Marcelo M. Amaral, Fang Fang and Klee Irwin
Symmetry 2020, 12(12), 1993; https://doi.org/10.3390/sym12121993 - 2 Dec 2020
Cited by 10 | Viewed by 5158
Abstract
We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature G=Z5⋊H where [...] Read more.
We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature G=Z5⋊H where H=Z2.S4≅2O is isomorphic to the binary octahedral group 2O and S4 is the symmetric group on four letters/bases. The second group has signature G=Z5⋊GL(2,3) and points out a threefold symmetry of base pairings. For those groups, the representations for the 22 conjugacy classes of G are in one-to-one correspondence with the multiplets encoding the proteinogenic amino acids. Additionally, most of the 22 characters of G attached to those representations are informationally complete. The biological meaning of these coincidences is discussed. Full article
(This article belongs to the Special Issue Emergent Order Parameters in Complex Biophysical Systems)
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17 pages, 4421 KiB  
Article
Interaction Patterns for Staggered Assembly of Fibrils from Semiflexible Chains
by Arnoud Jongeling, Carsten Svaneborg and Renko de Vries
Symmetry 2020, 12(11), 1926; https://doi.org/10.3390/sym12111926 - 23 Nov 2020
Viewed by 2067
Abstract
The design of colloidal interactions to achieve target self-assembled structures has especially been done for compact objects such as spheres with isotropic interaction potentials, patchy spheres and other compact objects with patchy interactions. Inspired by the self-assembly of collagen-I fibrils and intermediate filaments, [...] Read more.
The design of colloidal interactions to achieve target self-assembled structures has especially been done for compact objects such as spheres with isotropic interaction potentials, patchy spheres and other compact objects with patchy interactions. Inspired by the self-assembly of collagen-I fibrils and intermediate filaments, we here consider the design of interaction patterns on semiflexible chains that could drive their staggered assembly into regular (para)crystalline fibrils. We consider semiflexible chains composed of a finite number of types of interaction beads (uncharged hydrophilic, hydrophobic, positively charged and negatively charged) and optimize the sequence of these interaction beads with respect to the interaction energy of the semiflexible chains in a number of target-staggered crystalline packings. We find that structures with the lowest interaction energies, that form simple lattices, also have low values of L/D (where L is chain length and D is stagger). In the low interaction energy sequences, similar types of interaction beads cluster together to form stretches. Langevin Dynamics simulations confirm that semiflexible chains with optimal sequences self-assemble into the designed staggered (para)crystalline fibrils. We conclude that very simple interaction patterns should suffice to drive the assembly of long semiflexible chains into staggered (para)crystalline fibrils. Full article
(This article belongs to the Special Issue Emergent Order Parameters in Complex Biophysical Systems)
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