Publisher's Note: Nonequilibrium steady states in a model for prebiotic evolution [Phys. Rev. E<b>89</b>, 022725 (2014)]

Wynveen, A.; Fedorov, I. V.; Halleý, J. W.

doi:10.1103/physreve.90.029901

Cited by 4 publications

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“…The total energy E of any population {n m } of polymers in which n m is the number of polymers of type m is E = − lmax L=1 (L − 1)N L ∆. Here the N L = m of length L n m is the same set of macrovariables used in [5] and [6]. We denote the total number of polymers N in a sample by is N = lmax L=1 N L .…”

Section: Discussionmentioning

confidence: 99%

“…In each case we can then use (5) to evaluate the polymer length density distributions expected in those two equilibrium states. Because the systems of interest are not necessarily (and in fact are found not to be) in either kind of chemical equilibrium we used the experimentally observed values of the quantities N L (v p /V ) to evaluate Euclidean distance in the space of values of sets {N L v p /V } between the actual population set {N L v p /V } and the ones corresponding to the two kinds of equilibria given by (5) with β(e, ρ), µ(e, ρ) in the isolated case and with a fixed ambient β and µ(ρ) in the case in which the system is equilibrated to an external bath. Thus we define two Euclidean distances R L and R T in the l max dimensional space of sets {N L (v p /V )} which characterize how far the system of interest is from the two kinds of equilbria:…”

Section: Discussionmentioning

confidence: 99%

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Some generic measures of the extent of chemical disequilibrium applied to living and abiotic systems

Intoy

Halleý

2018

Preprint

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We report results of evaluation of several measures of chemical disequilibrium in living and abiotic systems. The previously defined measures include RT and RL which are Euclidean distances of a coarse grained polymer length distribution from two different chemical equilibrium states associated with equilibration to an external temperature bath and with isolated equilibration to a distribution determined by the bond energy of the system, respectively. The determination uses a simplified model of the energetics of the constituent molecules introduced earlier. We evaluated the measures for data from the ribosome of E. Coli, a variety of yeast, the proteomes (with certain assumptions) of a large family of prokaryotes, for mass spectrometric data from the atmosphere the Saturn satellite Titan and for commercial copolymers. We find with surprising consistency that RL is much smaller than RT for all these systems. Small RL may be characteristic of systems in the biosphere.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Some generic measures of the extent of chemical disequilibrium applied to living and abiotic systems

Intoy

Halleý

2018

Preprint

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“…As in our previous work [4], and following [5][6][7], the entities which we call 'polymers' or, equivalently 'molecules' in the model are strings of 0's and 1's which abstractly represent polymers built from two types of monomers. Further discussion of this choice appears in [4]. A qualitative 'roadmap' of the computations which we carry out in all the Kauffman like models which we have been studying for a single site is shown in figure 1.…”

Section: Modelmentioning

confidence: 99%

“…A qualitative 'roadmap' of the computations which we carry out in all the Kauffman like models which we have been studying for a single site is shown in figure 1. Given model parameters, namely p for the single island model of reference [4] and p and η for the model studied here, we first generate a large ensemble of 'artificial chemistries' numerically. The chemical constituents or species that are modeled as binary polymer strings may, in the model, undergo ligation and scission.…”

Section: Modelmentioning

confidence: 99%

“…However in studies of a model of prebiotic evolution on which we previously reported [4], the artificial chemical system was assumed to be 'well mixed' so that every molecule could react with every other one, as it is in many similar models [5] and explicit effects of any spatial heterogeneity were ignored. When metastable 'lifelike' states occurred in that model, they were protected from decay to equilibrium by bottlenecks in the dynamics of these states due to the sparseness of the network of chemical reactions without any explicit reference to space.…”

Section: Introductionmentioning

confidence: 99%

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Effects of spatial diffusion on nonequilibrium steady states in a model for prebiotic evolution

2016

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Effects of spatial diffusion in a Kauffman-like model for prebiotic evolution previously studied in a "well-mixed" limit are reported. The previous model was parametrized by a parameter p defined as the probability that a possible reaction in a network of reactions characterizing the artificial chemistry actually appears in the chemical network. In the model reported here, we numerically study a grid of such well-mixed reactors on a two-dimensional spatial lattice in which the model chemical constituents can hop between neighboring reactors at a rate controlled by a second parameter η. We report the frequency of appearance of three distinct types of nonequilibrium steady states, characterized as "diffusively alive locally dead" (DALD), "diffusively dead locally alive" (DDLA) and "diffusively alive locally alive" (DALA). The types are defined according to whether they are chemically equilibrated at each site, diffusively equilibrated between sites, or neither, respectively. With our parametrization of the definitions of these nonequilibrium states, many of the DALA states are growing rapidly in population due to the explosive population growth of a few sites, while their entropy remains well below its equilibrium value. Sharp temporal transitions occur as exploding sites appear. DALD states occur less commonly than the other types and also usually harbor a few explosively growing sites but transitions are less sharp than in DALA systems.

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Energetics in a model of prebiotic evolution

Intoy

Halleý

2017

Phys. Rev. E

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Previously we reported [A. Wynveen et al., Phys. Rev. E 89, 022725 (2014)PLEEE81539-375510.1103/PhysRevE.89.022725] that requiring that the systems regarded as lifelike be out of chemical equilibrium in a model of abstracted polymers undergoing ligation and scission first introduced by Kauffman [S. A. Kauffman, The Origins of Order (Oxford University Press, New York, 1993), Chap. 7] implied that lifelike systems were most probable when the reaction network was sparse. The model was entirely statistical and took no account of the bond energies or other energetic constraints. Here we report results of an extension of the model to include effects of a finite bonding energy in the model. We studied two conditions: (1) A food set is continuously replenished and the total polymer population is constrained but the system is otherwise isolated and (2) in addition to the constraints in (1) the system is in contact with a finite-temperature heat bath. In each case, detailed balance in the dynamics is guaranteed during the computations by continuous recomputation of a temperature [in case (1)] and of the chemical potential (in both cases) toward which the system is driven by the dynamics. In the isolated case, the probability of reaching a metastable nonequilibrium state in this model depends significantly on the composition of the food set, and the nonequilibrium states satisfying lifelike condition turn out to be at energies and particle numbers consistent with an equilibrium state at high negative temperature. As a function of the sparseness of the reaction network, the lifelike probability is nonmonotonic, as in our previous model, but the maximum probability occurs when the network is less sparse. In the case of contact with a thermal bath at a positive ambient temperature, we identify two types of metastable nonequilibrium states, termed locally and thermally alive, and locally dead and thermally alive, and evaluate their likelihood of appearance, finding maxima at an optimal temperature and an optimal degree of sparseness in the network. We use a Euclidean metric in the space of polymer populations to distinguish these states from one another and from fully equilibrated states. The metric can be used to characterize the degree and type of chemical equilibrium in observed systems, as we illustrate for the proteome of the ribosome.

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Publisher's Note: Nonequilibrium steady states in a model for prebiotic evolution [Phys. Rev. E89, 022725 (2014)]

Cited by 4 publications

References 0 publications

Some generic measures of the extent of chemical disequilibrium applied to living and abiotic systems

Some generic measures of the extent of chemical disequilibrium applied to living and abiotic systems

Effects of spatial diffusion on nonequilibrium steady states in a model for prebiotic evolution

Energetics in a model of prebiotic evolution

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