On the linear algebra of biological homochirality

Ágreda, Jesús; Mejía, Carolina; Montoya, J. Andres

doi:10.1007/s10910-018-0893-6

Cited by 4 publications

(6 citation statements)

References 9 publications

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“…The fourth algorithm is based on a condition occurring in the Frank network that creates symmetry-breaking states. This condition is nicknamed the Frank inequality [23] . All that is needed to find homochiral states in a chemical mechanism that has them is to sample solutions of the Frank inequality related to the network and explicitly computed by the algorithm.…”

Section: Methods Descriptionmentioning

confidence: 99%

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Linear stability analysis of chemical mechanism, Listanalchem: A tool for the search of spontaneous mirror symmetry breaking

Cruz,

Montoya,

Ágreda

2023

MethodsX

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Section: Methods Descriptionmentioning

confidence: 99%

“…This symmetry also exists in the original matrix but is hidden by the non-explicit equivalences of the dual pair conditions. This symmetry will play an essential role in the criterion called Frank inequality [23] , which is crucial in developing the last three algorithms.…”

Section: In-depth Description Of the Methods With Examplesmentioning

confidence: 99%

Linear stability analysis of chemical mechanism, Listanalchem: A tool for the search of spontaneous mirror symmetry breaking

Cruz,

Montoya,

Ágreda

2023

MethodsX

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“…It was observed that SMSB is still not possible according to SNA (see files Calvin-#-CSTR-Inhibition.py, second algorithm). However, when a more specific analysis is made, using the fifth [46] and sixth [33] Listanalchem algorithms, it was found that SMSB exists in versions 2 and 3 of the model (see files Calvin-2-CSTR-Inhibition.py and Calvin-3-CSTR-Inhibition.py, fifth and sixth algorithms), but it does not appear in version 1, see file Calvin-1-CSTR-Inhibition.py. This fact means that the heuristic (the work with the minors of the current matrix VΩ used in the second algorithm-SNA of Listanalchem to find the instability) is not 100 % effective, and some false negatives, like those presented before, are eventually obtained.…”

Section: Calvin Model 1969mentioning

confidence: 99%

Biological homochirality and stoichiometric network analysis: Variations on Frank’s model

Ágreda¹,

Montoya

Mejía³

2022

Rev. Colomb. Quim.

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Biological homochirality is modelled using chemical reaction mechanisms that include autocatalytic and inhibition reactions as well as input and output flows. From the mathematical point of view, the differential equations associated with those mechanisms have to exhibit bistability. The search for those bifurcations can be carried out using stoichiometric network analysis. This algorithm simplifies the mathematical analysis and can be implemented in a computer programme, which can help us to analyse chemical networks. However, regardless of the reduction to linear polynomials, which is made possible by this algorithm, in some cases, the complexity and length of the polynomials involved make the analysis unfeasible. This problem has been partially solved by extending the stoichiometric matrix with rows that code the duality relations between the different reactions occurring in the network given as input. All these facts allow us to analyse 28 different network models, highlighting the basic requirements needed by a chemical mechanism to have spontaneous mirror symmetry breaking.

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“…The existence of quantitative (analytical) solutions to these differential equations is desirable but limited to a small set of chemical networks [3]. Qualitative analysis, for example, linear stability analysis [4], Stoichiometric Network Analysis (SNA) [1,2], or more recently, Frank inequality for homochiral networks [5,6], gives us valuable information, but when the mechanisms involve many species and reactions, these qualitative analyses are hard to carry out. One more practical approach, although not a general solution, is to simulate the chemical network of interest under particular conditions.…”

Section: Chemical Kinetics Simulator (Chemkinlator): a Friendly User mentioning

confidence: 99%

CHEMical KINetics SimuLATOR (Chemkinlator): A friendly user interface for chemical kinetics simulations

Cruz¹,

Montoya²,

Ágreda³

2020

Rev. colomb. quim.

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CHEMical KINetics SimuLATOR is a Graphical User Interface for the simulation of reaction mechanisms. The interface allows the user to see and change the parameters of a reaction network within a single window. Chemkinlator comes with built-in support for three types of kinetic simulations: Time Series, which computes the concentration of all species in an interval of time in a defined model; Bifurcation diagrams, which are the result of running several Time Series simulations over gradually different kinetic rate constants; and Flow/Temperature time series, which takes into account the effect of flow in the Continuous-flow well-Stirred Tank Reactor, and the effect of temperature on the rates constants according to the Arrhenius equation. In our research group, Chemkinlator has been the primary tool used to test the predictions made by algorithms that analyze homochirality phenomena. Chemkinlator is written in C++14 and Qt, and it uses the Fortran subroutine DLSODE to solve the differential equations associated with the reaction networks. Chemkinlator is open source software under the Apache 2.0 license and can be downloaded freely from https://gitlab.com/homochirality/chemkinlator.

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On the linear algebra of biological homochirality

Cited by 4 publications

References 9 publications

Linear stability analysis of chemical mechanism, Listanalchem: A tool for the search of spontaneous mirror symmetry breaking

Linear stability analysis of chemical mechanism, Listanalchem: A tool for the search of spontaneous mirror symmetry breaking

Biological homochirality and stoichiometric network analysis: Variations on Frank’s model

CHEMical KINetics SimuLATOR (Chemkinlator): A friendly user interface for chemical kinetics simulations

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