scholarly journals Computing the Parameter Values for the Emergence of Homochirality in Complex Networks

Life ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 74
Author(s):  
Andrés Montoya ◽  
Elkin Cruz ◽  
Jesús Ágreda
Keyword(s):  
Symmetry Breaking ◽  
Heuristic Algorithm ◽  
Mirror Symmetry ◽  
Steady States ◽  
Chemical Mechanism ◽  
Reaction Networks ◽  
Nonlinear Character ◽  
Algorithmic Problems ◽  
Algorithmic Analysis ◽  
Parameter Values

The goal of our research is the development of algorithmic tools for the analysis of chemical reaction networks proposed as models of biological homochirality. We focus on two algorithmic problems: detecting whether or not a chemical mechanism admits mirror symmetry-breaking; and, given one of those networks as input, sampling the set of racemic steady states that can produce mirror symmetry-breaking. Algorithmic solutions to those two problems will allow us to compute the parameter values for the emergence of homochirality. We found a mathematical criterion for the occurrence of mirror symmetry-breaking. This criterion allows us to compute semialgebraic definitions of the sets of racemic steady states that produce homochirality. Although those semialgebraic definitions can be processed algorithmically, the algorithmic analysis of them becomes unfeasible in most cases, given the nonlinear character of those definitions. We use Clarke’s system of convex coordinates to linearize, as much as possible, those semialgebraic definitions. As a result of this work, we get an efficient algorithm that solves both algorithmic problems for networks containing only one enantiomeric pair and a heuristic algorithm that can be used in the general case, with two or more enantiomeric pairs.

scholarly journals Chemical Basis of Biological Homochirality during the Abiotic Evolution Stages on Earth

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 814 ◽  
Author(s):  
Josep M. Ribó ◽  
David Hochberg
Keyword(s):  
Symmetry Breaking ◽  
Chemical Evolution ◽  
Mirror Symmetry ◽  
Reaction Network ◽  
Reaction Networks ◽  
Stationary States ◽  
Cell Systems ◽  
Basic Model ◽  
Stochastic Distribution ◽  
Non Equilibrium

Spontaneous mirror symmetry breaking (SMSB), a phenomenon leading to non-equilibrium stationary states (NESS) that exhibits biases away from the racemic composition is discussed here in the framework of dissipative reaction networks. Such networks may lead to a metastable racemic non-equilibrium stationary state that transforms into one of two degenerate but stable enantiomeric NESSs. In such a bifurcation scenario, the type of the reaction network, as well the boundary conditions, are similar to those characterizing the currently accepted stages of emergence of replicators and autocatalytic systems. Simple asymmetric inductions by physical chiral forces during previous stages of chemical evolution, for example in astrophysical scenarios, must involve unavoidable racemization processes during the time scales associated with the different stages of chemical evolution. However, residual enantiomeric excesses of such asymmetric inductions suffice to drive the SMSB stochastic distribution of chiral signs into a deterministic distribution. According to these features, we propose that a basic model of the chiral machinery of proto-life would emerge during the formation of proto-cell systems by the convergence of the former enantioselective scenarios.

2,6-Dibromogallates as a new building block for controlling π-stacking, network formation and mirror symmetry breaking

2021 ◽  
Author(s):  
Ohjin Kwon ◽  
Xiaoqian Cai ◽  
Azhar Saeed ◽  
Feng Liu ◽  
Silvio Poppe ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Building Block ◽  
Mirror Symmetry ◽  
Network Formation ◽  
Network Structures ◽  
Π Stacking ◽  
Bicontinuous Cubic ◽  
Substituted 1 ◽  
End Group

Achiral multi-chain (polycatenar) compounds based on the 2,7-diphenyl substituted [1]benzothieno[3,2-b]benzothiophene (BTBT) unit and a 2,6-dibromo-3,4,5-trialkoxybenzoate end group lead to materials forming bicontinuous cubic liquid crystaline phases with helical network structures...

Symmetry-breaking bifurcations in resonant surface waves

1989 ◽  
Vol 199 ◽  
pp. 495-518 ◽  
Author(s):  
Z. C. Feng ◽  
P. R. Sethna
Keyword(s):  
Normal Form ◽  
Symmetry Breaking ◽  
Surface Waves ◽  
Bifurcation Analysis ◽  
Internal Resonance ◽  
Travelling Waves ◽  
Chaotic Behaviour ◽  
Derived Set ◽  
Parameter Values ◽  
Theoretical Results

Surface waves in a nearly square container subjected to vertical oscillations are studied. The theoretical results are based on the analysis of a derived set of normal form equations, which represent perturbations of systems with 1:1 internal resonance and with D4 symmetry. Bifurcation analysis of these equations shows that the system is capable of periodic and quasi-periodic standing as well as travelling waves. The analysis also identifies parameter values at which chaotic behaviour is to be expected. The theoretical results are verified with the aid of some experiments.

scholarly journals Families of toric chemical reaction networks

2020 ◽  
Vol 58 (9) ◽  
pp. 2061-2093
Author(s):  
Michael F. Adamer ◽  
Martin Helmer
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Steady States ◽  
Reaction Networks ◽  
Core Network ◽  
Entire Family ◽  
Data Set ◽  
The Family ◽  
Positive Steady States ◽  
State Behaviour

Abstract We study families of chemical reaction networks whose positive steady states are toric, and therefore can be parameterized by monomials. Families are constructed algorithmically from a core network; we show that if a family member is multistationary, then so are all subsequent networks in the family. Further, we address the questions of model selection and experimental design for families by investigating the algebraic dependencies of the chemical concentrations using matroids. Given a family with toric steady states and a constant number of conservation relations, we construct a matroid that encodes important information regarding the steady state behaviour of the entire family. Among other things, this gives necessary conditions for the distinguishability of families of reaction networks with respect to a data set of measured chemical concentrations. We illustrate our results using multi-site phosphorylation networks.

Reply to “Mirror Symmetry Breaking” of the Centrosymmetric CaCO3 Crystals with Amino Acids

2008 ◽  
Vol 120 (20) ◽  
pp. 3741-3744
Author(s):  
Niklas Loges ◽  
Stephan E. Wolf ◽  
Martin Panthöfer ◽  
Lars Müller ◽  
Marc-Christopher Reinnig ◽  
...  
Keyword(s):  
Amino Acids ◽  
Symmetry Breaking ◽  
Mirror Symmetry

scholarly journals Entropic Analysis of Mirror Symmetry Breaking in Chiral Hypercycles

Life ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 28 ◽  
Author(s):  
David Hochberg ◽  
Josep Ribó
Keyword(s):  
Symmetry Breaking ◽  
Entropy Production ◽  
Mirror Symmetry ◽  
Flow Reactor ◽  
Evolutionary Selection ◽  
Replicator System ◽  
Stoichiometric Network Analysis ◽  
Underlying Mechanisms ◽  
The Individual ◽  
Origin Of Homochirality

Replicators are fundamental to the origin of life and evolvability. Biology exhibits homochirality: only one of two enantiomers is used in proteins and nucleic acids. Thermodynamic studies of chemical replicators able to lead to homochirality shed valuable light on the origin of homochirality and life in conformity with the underlying mechanisms and constraints. In line with this framework, enantioselective hypercyclic replicators may lead to spontaneous mirror symmetry breaking (SMSB) without the need for additional heterochiral inhibition reactions, which can be an obstacle for the emergence of evolutionary selection properties. We analyze the entropy production of a two-replicator system subject to homochiral cross-catalysis which can undergo SMSB in an open-flow reactor. The entropy exchange with the environment is provided by the input and output matter flows, and is essential for balancing the entropy production at the non-equilibrium stationary states. The partial entropy contributions, associated with the individual elementary flux modes, as defined by stoichiometric network analysis (SNA), describe how the system’s internal currents evolve, maintaining the balance between entropy production and exchange, while minimizing the entropy production after the symmetry breaking transition. We validate the General Evolution Criterion, stating that the change in the chemical affinities proceeds in a way as to lower the value of the entropy production.

Sign in / Sign up

Export Citation Format

Share Document