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25 pages, 4492 KB  
Article
Template-Based Catalysis and the Emergence of Collectively Autocatalytic Systems
by Roberto Serra and Marco Villani
Entropy 2026, 28(2), 184; https://doi.org/10.3390/e28020184 - 6 Feb 2026
Viewed by 352
Abstract
Mathematical and computational models, which have been successfully used in various fields of biology, are particularly relevant in studies on the origin of life, where wet experiments have not yet been able to obtain fully “living” entities from abiotic materials. This paper investigates [...] Read more.
Mathematical and computational models, which have been successfully used in various fields of biology, are particularly relevant in studies on the origin of life, where wet experiments have not yet been able to obtain fully “living” entities from abiotic materials. This paper investigates mathematical and computational models of interacting polymers in prebiotic environments to understand how molecular replication and protocell reproduction could emerge. This study builds on the Binary Polymer Model (K-BPM), in which polymers are represented as binary strings that undergo catalyzed condensation and cleavage reactions, by introducing a biologically relevant variant (C-BPM), where catalytic activity depends on polymer structure. The model is analyzed with respect to the formation of autocatalytic networks, formalized as Reflexive Autocatalytic Food-generated (RAF) sets, embedded in a protocell in order to simulate their dynamics. The results show clear differences between K-BPM and C-BPM models. They also show that the existence of a RAF does not guarantee the survival of a population of protocells, although it may be possible when only a subset of the existing species partakes in the RAF, thus suggesting that small autocatalytic networks may have preceded the larger networks found in modern life. Full article
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36 pages, 4531 KB  
Review
Fascinating Frontier, Nanoarchitectonics, as Method for Everything in Materials Science
by Katsuhiko Ariga
Materials 2025, 18(22), 5196; https://doi.org/10.3390/ma18225196 - 15 Nov 2025
Cited by 5 | Viewed by 979
Abstract
Methodological fusion of materials chemistry, which enables us to create materials, with nanotechnology, which enables us to control nanostructures, could enable us to create advanced functional materials with well controlled nanostructures. Positioned as a post-nanotechnology concept, nanoarchitectonics will enable this purpose. This review [...] Read more.
Methodological fusion of materials chemistry, which enables us to create materials, with nanotechnology, which enables us to control nanostructures, could enable us to create advanced functional materials with well controlled nanostructures. Positioned as a post-nanotechnology concept, nanoarchitectonics will enable this purpose. This review paper highlights the broad scope of applications of the new concept of nanoarchitectonics, selecting and discussing recent papers that contain the term ‘nanoarchitectonics’ in their titles. Topics include controls of dopant atoms in solid electrolytes, transforming the framework of carbon materials, single-atom catalysts, nanorobots and microrobots, functional nanoparticles, nanotubular materials, 2D-organic nanosheets and MXene nanosheets, nanosheet assemblies, nitrogen-doped carbon, nanoporous and mesoporous materials, nanozymes, polymeric materials, covalent organic frameworks, vesicle structures from synthetic polymers, chirality- and topology-controlled structures, chiral helices, Langmuir monolayers, LB films, LbL assembly, nanocellulose, DNA, peptides bacterial cell components, biomimetic nanoparticles, lipid membranes of protocells, organization of living cells, and the encapsulation of living cells with exogenous substances. Not limited to these examples selected in this review article, the concept of nanoarchitectonics is applicable to diverse materials systems. Nanoarchitectonics represents a conceptual framework for creating materials at all levels and can be likened to a method for everything in materials science. Developing technology that can universally create materials with unexpected functions could represent the final frontier of materials science. Nanoarchitectonics will play a significant part in achieving this final frontier in materials science. Full article
(This article belongs to the Special Issue Nanoarchitectonics in Materials Science, Second Edition)
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17 pages, 7498 KB  
Review
A Recipe to Evolve Complex Life Chemically on Earth
by Lei Lei and Zachary Frome Burton
Genes 2025, 16(10), 1136; https://doi.org/10.3390/genes16101136 - 25 Sep 2025
Viewed by 1319
Abstract
Sequences of tRNAs are highly patterned in easily identifiable RNA repeats and RNA inverted repeats (stem–loop–stems). Because of patterning, the multi-step evolution of tRNA can be described in remarkable detail. To evolve life on Earth or another planet or the moon requires the [...] Read more.
Sequences of tRNAs are highly patterned in easily identifiable RNA repeats and RNA inverted repeats (stem–loop–stems). Because of patterning, the multi-step evolution of tRNA can be described in remarkable detail. To evolve life on Earth or another planet or the moon requires the evolution of tRNA or a tRNA-like molecule to act as a genetic adapter. To replace tRNA with an alternate or improved genetic adapter is a remarkably challenging problem, indicating strong chemical selection of tRNA precursors in pre-life. The genetic code, translation systems, and first proteins coevolved with tRNAomes (all of the tRNAs of an organism). Because the tRNA sequence can be separated into component parts, a simple pathway for chemical evolution of life and genetic coding can be described in sufficient detail to allow the assembly of a living entity in laboratories. Full article
(This article belongs to the Special Issue Roles of RNAs in Biology)
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24 pages, 3829 KB  
Article
Protocell Dynamics: Modelling Growth and Division of Lipid Vesicles Driven by an Autocatalytic Reaction
by Japraj Taneja and Paul G. Higgs
Life 2025, 15(5), 724; https://doi.org/10.3390/life15050724 - 29 Apr 2025
Viewed by 2669
Abstract
We study a computational model of a protocell, in which an autocatalytic reaction sustains itself inside a lipid vesicle. The autocatalytic reaction drives volume growth via osmosis. Membrane area grows due to addition of lipids from the environment. The membrane growth rate depends [...] Read more.
We study a computational model of a protocell, in which an autocatalytic reaction sustains itself inside a lipid vesicle. The autocatalytic reaction drives volume growth via osmosis. Membrane area grows due to addition of lipids from the environment. The membrane growth rate depends on the external lipid concentration and on the tension in the membrane. In the absence of division, a cell either reaches a state of homeostasis or grows to a point where the internal reaction collapses. If a cell becomes elongated, it can divide into two smaller spherical vesicles, conserving the total volume and area. We determine when it is energetically favorable for a large vesicle to divide. Division requires the buildup of a difference between the lipid areas on the outer and inner leaflets of the membrane. Division occurs most easily when the rate of flipping of lipids between leaflets is relatively slow. If the flipping is too fast, the parent cell grows large without dividing. There is a typical size at which division occurs, producing two daughter cells of unequal sizes. The smaller and larger daughters regrow to the same typical size before the next division. Protocells with an active metabolism reach a stable state where the internal autocatalytic reaction and the membrane growth are well balanced. Active protocells can grow and divide in conditions where an inactive vesicle without an internal reaction cannot. Full article
(This article belongs to the Special Issue 2nd Edition—Featured Papers on the Origins of Life)
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22 pages, 3826 KB  
Review
Silicasomes in Oncology: From Conventional Chemotherapy to Combined Immunotherapy
by Alicia Arroyo-Nogales, Guillermo Plaza-Palomo, Javier González-Larre, Sandra Jiménez-Falcao and Alejandro Baeza
Molecules 2025, 30(6), 1257; https://doi.org/10.3390/molecules30061257 - 11 Mar 2025
Cited by 4 | Viewed by 1741
Abstract
The use of nanoparticles as drug carriers in oncology has evolved from their traditional role as chemotherapy carriers to their application in immunotherapy, exploiting not only their passive accumulation in solid tumors but also their ability to interact with immune cells. Silicasomes are [...] Read more.
The use of nanoparticles as drug carriers in oncology has evolved from their traditional role as chemotherapy carriers to their application in immunotherapy, exploiting not only their passive accumulation in solid tumors but also their ability to interact with immune cells. Silicasomes are highly versatile nanoplatforms composed of a mesoporous silica core whose external surface is coated with a lipid bilayer that allows the co-delivery of therapeutic agents having different chemical natures (small molecules, proteins, enzymes, or oligonucleotides, among others). Herein, cutting-edge advances carried out in the development and application of silicasomes are presented, providing a general description of the performance of these nanotransporters. Additionally, the specific load of chemotherapeutic drugs is explored, followed by a discussion of the immunotherapeutic application of silicasomes and the combination of different therapeutic strategies, including theragnosis, in a single silicasome platform, highlighting the enormous potential of these nanosystems. Full article
(This article belongs to the Section Nanochemistry)
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26 pages, 56274 KB  
Review
Chemical Evolution of Life on Earth
by Lei Lei and Zachary Frome Burton
Genes 2025, 16(2), 220; https://doi.org/10.3390/genes16020220 - 13 Feb 2025
Cited by 1 | Viewed by 5856
Abstract
Background/Objectives: The origin of genes and genetics is the story of the coevolution of translation systems and the genetic code. Remarkably, the history of the origin of life on Earth was inscribed and preserved in the sequences of tRNAs. Methods: Sequence [...] Read more.
Background/Objectives: The origin of genes and genetics is the story of the coevolution of translation systems and the genetic code. Remarkably, the history of the origin of life on Earth was inscribed and preserved in the sequences of tRNAs. Methods: Sequence logos demonstrate the patterning of pre-life tRNA sequences. Results: The pre-life type I and type II tRNA sequences are known to the last nucleotide with only a few ambiguities. Type I and type II tRNAs evolved from ligation of three 31 nt minihelices of highly patterned and known sequence followed by closely related 9 nt internal deletion(s) within ligated acceptor stems. The D loop 17 nt core was a truncated UAGCC repeat. The anticodon and T 17 nt stem-loop-stems are homologous sequences with 5 nt stems and 7 nt U-turn loops that were selected in pre-life to resist ribozyme nucleases and to present a 3 nt anticodon with a single wobble position. The 7 nt T loop in tRNA was selected to interact with the D loop at the “elbow”. The 5′-acceptor stem was based on a 7 nt truncated GCG repeat. The 3′-acceptor stem was based on a complementary 7 nt CGC repeat. In pre-life, ACCA-Gly was a primitive adapter molecule ligated to many RNAs, including tRNAs, to synthesize polyglycine. Conclusions: Analysis of sequence logos of tRNAs from an ancient Archaeon substantiates how the pre-life to life transition occurred on Earth. Polyglycine is posited to have aggregated complex molecular assemblies, including minihelices, tRNAs, cooperating molecules, and protocells, leading to the first life on Earth. Full article
(This article belongs to the Section Population and Evolutionary Genetics and Genomics)
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13 pages, 3051 KB  
Hypothesis
On the Origin of Information Dynamics in Early Life
by Robert A. Gatenby, Jill Gallaher, Hemachander Subramanian, Emma U. Hammarlund and Christopher J. Whelan
Life 2025, 15(2), 234; https://doi.org/10.3390/life15020234 - 5 Feb 2025
Cited by 1 | Viewed by 2424
Abstract
We hypothesize that predictable variations in environmental conditions caused by night/day cycles created opportunities and hazards that initiated information dynamics central to life’s origin. Increased daytime temperatures accelerated key chemical reactions but also caused the separation of double-stranded polynucleotides, leading to hydrolysis, particularly [...] Read more.
We hypothesize that predictable variations in environmental conditions caused by night/day cycles created opportunities and hazards that initiated information dynamics central to life’s origin. Increased daytime temperatures accelerated key chemical reactions but also caused the separation of double-stranded polynucleotides, leading to hydrolysis, particularly of single-stranded RNA. Daytime solar UV radiation promoted the synthesis of organic molecules but caused broad damage to protocell macromolecules. We hypothesize that inter-related simultaneous adaptations to these hazards produced molecular dynamics necessary to store and use information. Self-replicating RNA heritably reduced the hydrolysis of single strands after separation during warmer daytime periods by promoting sequences that formed hairpin loops, generating precursors to transfer RNA (tRNA), and initiating tRNA-directed evolutionary dynamics. Protocell survival during daytime promoted sequences in self-replicating RNA within protocells that formed RNA–peptide hybrids capable of scavenging UV-induced free radicals or catalyzing melanin synthesis from tyrosine. The RNA–peptide hybrids are precursors to ribosomes and the triplet codes for RNA-directed protein synthesis. The protective effects of melanin production persist as melanosomes are found throughout the tree of life. Similarly, adaptations mitigating UV damage led to the replacement of Na+ by K+ as the dominant mobile cytoplasmic cation to promote diel vertical migration and selected for homochirality. We conclude that information dynamics emerged in early life through adaptations to predictably fluctuating opportunities and hazards during night/day cycles, and its legacy remains observable in extant life. Full article
(This article belongs to the Section Astrobiology)
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15 pages, 4130 KB  
Article
Protocells Either Synchronize or Starve
by Marco Villani and Roberto Serra
Entropy 2025, 27(2), 154; https://doi.org/10.3390/e27020154 - 2 Feb 2025
Cited by 1 | Viewed by 1302
Abstract
Two different processes take place in self-reproducing protocells, i.e., (i) cell reproduction by fission and (ii) duplication of the genetic material. One major problem is indeed that of assuring that the two processes take place at the same pace, i.e., that they synchronize, [...] Read more.
Two different processes take place in self-reproducing protocells, i.e., (i) cell reproduction by fission and (ii) duplication of the genetic material. One major problem is indeed that of assuring that the two processes take place at the same pace, i.e., that they synchronize, which is a necessary condition for sustainable growth. In previous theoretical works, using dynamical models, we had shown that such synchronization can spontaneously emerge, generation after generation, under a broad set of hypotheses about the architecture of the protocell, the nature of the self-replicating molecules, and the types of kinetic equations. However, an important class of cases (quadratic or higher-order self-replication) did not synchronize in the models we had used, but could actually lead to divergence of the concentration of replicators. We show here that this behavior is due to a simplification of the previous models, i.e., the “buffering” hypothesis, which assumes instantaneous equilibrium of the internal and external concentrations of those compounds which can cross the cell membrane. That divergence disappears if we make use of more realistic dynamical models, with finite transmembrane diffusion rates of the precursors of replicators. Full article
(This article belongs to the Section Entropy and Biology)
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12 pages, 2148 KB  
Article
A New Means to Generate Liposomes by Rehydrating Engineered Lipid Nanoconstructs
by Yuqi Huang, Ziqian Xu, Umit Celik, Christopher F. Carnahan, Roland Faller, Atul N. Parikh and Gang-yu Liu
Micromachines 2025, 16(2), 138; https://doi.org/10.3390/mi16020138 - 25 Jan 2025
Cited by 1 | Viewed by 1782
Abstract
The concept and feasibility of producing liposomes by rehydrating engineered lipid nanoconstructs are demonstrated in this study. Nanoconstructs of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) were produced using a microfluidic delivery probe integrated with an atomic force microscope. The subsequent rehydration of these POPC constructs led to [...] Read more.
The concept and feasibility of producing liposomes by rehydrating engineered lipid nanoconstructs are demonstrated in this study. Nanoconstructs of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) were produced using a microfluidic delivery probe integrated with an atomic force microscope. The subsequent rehydration of these POPC constructs led to the formation of liposomes, most of which remained adhered to the surface. The size (e.g., diameter) of the liposomes could be tuned by varying the lateral dimension of the lipid constructs. Hierarchical liposomal structures, such as pentagons containing five liposomes at the corners, could also be designed and produced by depositing lipid constructs to designated locations on the surfaces, followed by rehydration. This new means allows for regulating liposomal sizes, distributions, and compositions. The outcomes benefit applications of liposomes as delivery vehicles, sensors, and building blocks in biomaterials design. The ability to produce hierarchical liposomal structures benefits numerous applications such as proto-cell development, multiplexed bio-composite materials, and the engineering of local bio-environments. Full article
(This article belongs to the Collection Women in Micromachines)
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14 pages, 2106 KB  
Article
Thermodynamics of Morphogenesis: Beading and Branching Pattern Formation in Diffusion-Driven Salt Finger Plumes
by Hisashi Ozawa, Sayaka Murayama-Ogino and Axel Kleidon
Entropy 2025, 27(2), 106; https://doi.org/10.3390/e27020106 - 22 Jan 2025
Cited by 1 | Viewed by 1392
Abstract
Spontaneous pattern formation is a universal phenomenon that occurs in purely physical systems, biology, and human societies. Salt fingering due to differential diffusion of heat and salt in seawater is a typical example, although the general principle that governs pattern formation remains unknown. [...] Read more.
Spontaneous pattern formation is a universal phenomenon that occurs in purely physical systems, biology, and human societies. Salt fingering due to differential diffusion of heat and salt in seawater is a typical example, although the general principle that governs pattern formation remains unknown. We show through simple experiments injecting a salt solution into a sucrose solution of equal density that a salt finger exhibits characteristic pattern transitions depending on the injection flow rate. When the rate increases, a linear finger starts meandering, branching, and multiple branching, whereas when the rate is decreased, it produces a beading pattern. These morphological instabilities and associated pattern formation are caused by a local accumulation of kinetic energy that minimizes the flow resistance and maximizes the energy dissipation in the final steady state. We suggest that this energy accumulation mechanism governs a wide variety of pattern formation phenomena in non-equilibrium systems, including morphogenesis of abiotic protocells. Full article
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16 pages, 1216 KB  
Article
The Origin(s) of LUCA: Computer Simulation of a New Theory
by Shiping Tang and Ming Gao
Life 2025, 15(1), 75; https://doi.org/10.3390/life15010075 - 10 Jan 2025
Cited by 2 | Viewed by 4582
Abstract
Carl Woese’s thesis of cellular evolution emphasized that the last universal common/cellular ancestor (LUCA) must have evolved by drawing from “global inventions”. Yet, existing theories regarding the origin(s) of LUCA have mostly centered upon scenarios that LUCA had evolved mostly independently. In an [...] Read more.
Carl Woese’s thesis of cellular evolution emphasized that the last universal common/cellular ancestor (LUCA) must have evolved by drawing from “global inventions”. Yet, existing theories regarding the origin(s) of LUCA have mostly centered upon scenarios that LUCA had evolved mostly independently. In an earlier paper, we advanced a new theory regarding the origin(s) of LUCA that extends Woese’s original insights. Our theory centers upon the possibility that different vesicles and protocells can merge with and acquire each other as a form of variation, selection, and retention, driven by wet-and-dry cycles and other similar cyclical processes. In this paper, we use computer simulation to show that under a variety of simulated conditions, LUCA can indeed be produced by our proposed processes. We hope that our study can stimulate laboratory testing of some key hypotheses that vesicles’ absorption, acquisition, and merger has indeed been a central force in driving the evolution of LUCA. Full article
(This article belongs to the Special Issue Origin of Life in Chemically Complex Messy Environments: 2nd Edition)
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32 pages, 7451 KB  
Article
The Possible Crystallization Process in the Origin of Bacteria, Archaea, Viruses, and Mobile Elements
by Akari Yoshimura and Masayuki Seki
Biology 2025, 14(1), 3; https://doi.org/10.3390/biology14010003 - 24 Dec 2024
Viewed by 2243
Abstract
We propose a hypothesis for the simultaneous emergence of bacteria, archaea, viruses, and mobile elements by sequential and concrete biochemical pathways. The emergence process can be considered analogous to crystallization, where genetic and biochemical systems stabilize as organisms evolve from their common ancestor, [...] Read more.
We propose a hypothesis for the simultaneous emergence of bacteria, archaea, viruses, and mobile elements by sequential and concrete biochemical pathways. The emergence process can be considered analogous to crystallization, where genetic and biochemical systems stabilize as organisms evolve from their common ancestor, the LUCA, which was a non-free-living pool of single operon type genomes including double-stranded (ds) DNA at an ancient submarine alkaline vent. Each dsDNA operon was transcribed by different systems in σ, TFIIB, or TBP genomes. Double-stranded DNA operons can fuse and stabilize through the action of specific transcription systems, leading to differentiation between the Bacteria (σ genome) and Archaea (TBP genome) domains. Error catastrophe can be overcome by the parallel gain of DNA replication and DNA repair mechanisms in both genomes. Enlarged DNA enabled efficient local biochemical reactions. Both genomes independently recruited lipids to facilitate reactions by forming coacervates at the chamber of the vent. Bilayer lipid membrane formation, proto-cell formation with a permeable membrane, proto-cell division, and the evolution of membrane-associated biochemistry are presented in detail. Simultaneous crystallization of systems in non-free-living bacteria and non-free-living archaea triggered the co-crystallization of primitive viruses and mobile elements. An arms race between non-free-living cells and primitive viruses finally led to free-living cells with a cell wall and mature viruses. Full article
(This article belongs to the Section Evolutionary Biology)
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13 pages, 7925 KB  
Article
Information Gradient among Nucleotide Sequences of Essential RNAs from an Evolutionary Perspective
by Houssem Ben Khalfallah, Mariem Jelassi, Hajar Rissaoui, Mohtadi Barchouchi, Clément Baraille, Joël Gardes and Jacques Demongeot
Int. J. Mol. Sci. 2024, 25(14), 7521; https://doi.org/10.3390/ijms25147521 - 9 Jul 2024
Cited by 2 | Viewed by 1564
Abstract
We hypothesize that the first ancestral “protocell” molecular structures, i.e., the first RNAs and peptides that gradually transformed into real cells once the Earth had cooled sufficiently for organic molecules to appear, have left traces in the RNAs and the genes in present [...] Read more.
We hypothesize that the first ancestral “protocell” molecular structures, i.e., the first RNAs and peptides that gradually transformed into real cells once the Earth had cooled sufficiently for organic molecules to appear, have left traces in the RNAs and the genes in present cells. We propose a circular RNA that could have been one of these ancestral structures whose vestigial pentameric subsequences would mark the evolution from this key moment when the protocells began to join with living organisms. In particular, we propose that, in present RNAs (ribosomal or messenger), which play an important role in the metabolism of current cells, we look for traces of the proposed primitive structure in the form of pentamers (or longer fragments) that belong to their nucleotide sequence. The result obtained can be summarized in the existence of a gradient of occurrence of such pentamers, with a high frequency for the most vital functions (protein synthesis, nucleic synthesis, cell respiration, etc.). This gradient is also visible between organisms, from the oldest (Archaea) to the most recent (Eukaryotes) in the evolution of species. Full article
(This article belongs to the Section Molecular Biology)
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15 pages, 6633 KB  
Article
A Fusion–Growth Protocell Model Based on Vesicle Interactions with Pyrite Particles
by Dong Guo, Ziyue Zhang, Jichao Sun, Hui Zhao, Wanguo Hou and Na Du
Molecules 2024, 29(11), 2664; https://doi.org/10.3390/molecules29112664 - 4 Jun 2024
Viewed by 2422
Abstract
Protocell models play a pivotal role in the exploration of the origin of life. Vesicles are one type of protocell model that have attracted much attention. Simple single-chain amphiphiles (SACs) and organic small molecules (OSMs) possess primitive relevance and were most likely the [...] Read more.
Protocell models play a pivotal role in the exploration of the origin of life. Vesicles are one type of protocell model that have attracted much attention. Simple single-chain amphiphiles (SACs) and organic small molecules (OSMs) possess primitive relevance and were most likely the building blocks of protocells on the early Earth. OSM@SAC vesicles have been considered to be plausible protocell models. Pyrite (FeS2), a mineral with primitive relevance, is ubiquitous in nature and plays a crucial role in the exploration of the origin of life in the mineral–water interface scenario. “How do protocell models based on OSM@SAC vesicles interact with a mineral–water interface scenario that simulates a primitive Earth environment” remains an unresolved question. Hence, we select primitive relevant sodium monododecyl phosphate (SDP), isopentenol (IPN) and pyrite (FeS2) mineral particles to build a protocell model. The model investigates the basic physical and chemical properties of FeS2 particles and reveals the effects of the size, content and duration of interaction of FeS2 particles on IPN@SDP vesicles. This deepens the understanding of protocell growth mechanisms in scenarios of mineral–water interfaces in primitive Earth environments and provides new information for the exploration of the origin of life. Full article
(This article belongs to the Special Issue Amphiphilic Molecules, Interfaces and Colloids)
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18 pages, 3583 KB  
Article
Models of Protocells Undergoing Asymmetrical Division
by Marco Villani, Elena Alboresi and Roberto Serra
Entropy 2024, 26(4), 281; https://doi.org/10.3390/e26040281 - 26 Mar 2024
Cited by 3 | Viewed by 1750
Abstract
The conditions that allow for the sustained growth of a protocell population are investigated in the case of asymmetrical division. The results are compared to those of previous studies concerning models of symmetrical division, where synchronization (between duplication of the genetic material and [...] Read more.
The conditions that allow for the sustained growth of a protocell population are investigated in the case of asymmetrical division. The results are compared to those of previous studies concerning models of symmetrical division, where synchronization (between duplication of the genetic material and fission of the lipid container) was found under a variety of different assumptions about the kinetic equations and about the place where molecular replication takes place. Such synchronization allows a sustained proliferation of the protocell population. In the asymmetrical case, there can be no true synchronization, since the time to duplication may depend upon the initial size, but we introduce a notion of homogeneous growth that actually allows for the sustained reproduction of a population of protocells. We first analyze Surface Reaction Models, defined in the text, and we show that in many cases they undergo homogeneous growth under the same kinetic laws that lead to synchronization in the symmetrical case. This is the case also for Internal Reaction Models (IRMs), which, however, require a deeper understanding of what homogeneous growth actually means, as discussed below. Full article
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