A Polyaddition Model for the Prebiotic Polymerization of RNA and RNA-Like Polymers

Implicit in the RNA world hypothesis is that prebiotic RNA synthesis, despite occurring in an environment without biochemical catalysts, produced the long RNA polymers which are essential to the formation of life. In order to investigate the prebiotic formation of long RNA polymers, we consider a general solution of functionally identical monomer units that are capable of bonding to form linear polymers by a step-growth process. Under the assumptions that (1) the solution is well-mixed and (2) bonding/unbonding rates are independent of polymerization state, the concentration of each length of polymer follows the geometric Flory-Schulz distribution. We consider the rate dynamics that produce this equilibrium; connect the rate dynamics, Gibbs free energy of bond formation, and the bonding probability; solve the dynamics in closed form for the representative special case of a Flory-Schulz initial condition; and demonstrate the effects of imposing a maximum polymer length. Afterwards, we derive a lower bound on the error introduced by truncation and compare this lower bound to the actual error found in our simulation. Finally, we suggest methods to connect these theoretical predictions to experimental results.

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Randomness and Complexity

10.1093/oso/9780198814825.003.0007 ◽

2018 ◽

Author(s):

Steven E. Vigdor

Keyword(s):

Quantum Mechanics ◽

Natural Selection ◽

Rna World ◽

Biological Evolution ◽

Variable Theory ◽

Cosmological Natural Selection ◽

Einstein Podolsky Rosen ◽

World Hypothesis ◽

Rna World Hypothesis

Chapter 7 describes the fundamental role of randomness in quantum mechanics, in generating the first biomolecules, and in biological evolution. Experiments testing the Einstein–Podolsky–Rosen paradox have demonstrated, via Bell’s inequalities, that no local hidden variable theory can provide a viable alternative to quantum mechanics, with its fundamental randomness built in. Randomness presumably plays an equally important role in the chemical assembly of a wide array of polymer molecules to be sampled for their ability to store genetic information and self-replicate, fueling the sort of abiogenesis assumed in the RNA world hypothesis of life’s beginnings. Evidence for random mutations in biological evolution, microevolution of both bacteria and antibodies and macroevolution of the species, is briefly reviewed. The importance of natural selection in guiding the adaptation of species to changing environments is emphasized. A speculative role of cosmological natural selection for black-hole fecundity in the evolution of universes is discussed.

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A Note on a Lower Bound for the Multiplicative Odds Theorem of Optimal Stopping

Journal of Applied Probability ◽

10.1017/s0021900200011748 ◽

2014 ◽

Vol 51 (03) ◽

pp. 885-889 ◽

Cited By ~ 1

Author(s):

Tomomi Matsui ◽

Katsunori Ano

Keyword(s):

Lower Bound ◽

Optimal Stopping ◽

Secretary Problem ◽

Bernoulli Trials ◽

Optimal Stopping Problem ◽

Maximum Probability ◽

Optimal Stopping Rule ◽

Optimal Probability ◽

Optimal Stopping Theory ◽

Special Case

In this note we present a bound of the optimal maximum probability for the multiplicative odds theorem of optimal stopping theory. We deal with an optimal stopping problem that maximizes the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length N, where m and N are predetermined integers satisfying 1 ≤ m < N. This problem is an extension of Bruss' (2000) odds problem. In a previous work, Tamaki (2010) derived an optimal stopping rule. We present a lower bound of the optimal probability. Interestingly, our lower bound is attained using a variation of the well-known secretary problem, which is a special case of the odds problem.

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Improved bounds for the availability and unavailability in a fixed time interval for systems of maintained, interdependent components

Advances in Applied Probability ◽

10.1017/s0001867800033462 ◽

1980 ◽

Vol 12 (01) ◽

pp. 200-221 ◽

Cited By ~ 9

Author(s):

B. Natvig

Keyword(s):

Lower Bound ◽

System Reliability ◽

Nuclear Reactors ◽

Random Variables ◽

Fixed Time ◽

Time Interval ◽

Coherent System ◽

Exact Results ◽

Fixed Time Interval ◽

Special Case

In this paper we arrive at a series of bounds for the availability and unavailability in the time interval I = [t A , t B ] ⊂ [0, ∞), for a coherent system of maintained, interdependent components. These generalize the minimal cut lower bound for the availability in [0, t] given in Esary and Proschan (1970) and also most bounds for the reliability at time t given in Bodin (1970) and Barlow and Proschan (1975). In the latter special case also some new improved bounds are given. The bounds arrived at are of great interest when trying to predict the performance process of the system. In particular, Lewis et al. (1978) have revealed the great need for adequate tools to treat the dependence between the random variables of interest when considering the safety of nuclear reactors. Satyanarayana and Prabhakar (1978) give a rapid algorithm for computing exact system reliability at time t. This can also be used in cases where some simpler assumptions on the dependence between the components are made. It seems, however, impossible to extend their approach to obtain exact results for the cases treated in the present paper.

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Lower bounds for cutting planes proofs with small coefficients

Journal of Symbolic Logic ◽

10.2307/2275569 ◽

1997 ◽

Vol 62 (3) ◽

pp. 708-728 ◽

Cited By ~ 55

Author(s):

Maria Bonet ◽

Toniann Pitassi ◽

Ran Raz

Keyword(s):

Lower Bound ◽

Lower Bounds ◽

Cutting Planes ◽

Communication Complexity ◽

Proof System ◽

Small Weight ◽

Deduction Rule ◽

Special Case ◽

Exponential Lower Bound

AbstractWe consider small-weight Cutting Planes (CP*) proofs; that is, Cutting Planes (CP) proofs with coefficients up to Poly(n). We use the well known lower bounds for monotone complexity to prove an exponential lower bound for the length of CP* proofs, for a family of tautologies based on the clique function. Because Resolution is a special case of small-weight CP, our method also gives a new and simpler exponential lower bound for Resolution.We also prove the following two theorems: (1) Tree-like CP* proofs cannot polynomially simulate non-tree-like CP* proofs. (2) Tree-like CP* proofs and Bounded-depth-Frege proofs cannot polynomially simulate each other.Our proofs also work for some generalizations of the CP* proof system. In particular, they work for CP* with a deduction rule, and also for any proof system that allows any formula with small communication complexity, and any set of sound rules of inference.

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Transcription and translation in an RNA world

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2006.1910 ◽

2006 ◽

Vol 361 (1474) ◽

pp. 1751-1760 ◽

Cited By ~ 8

Author(s):

William R Taylor

Keyword(s):

Amino Acid ◽

Active Site ◽

Rna World ◽

Large Subunit ◽

Trna Synthetase ◽

Nucleoside Triphosphate ◽

Amino Acid Binding ◽

World Hypothesis ◽

Protein Elongation ◽

Rna World Hypothesis

The RNA world hypothesis requires a ribozyme that was an RNA-directed RNA polymerase (ribopolymerase). If such a replicase makes a reverse complementary copy of any sequence (including itself), in a simple RNA world, there is no mechanism to prevent self-hybridization. It is proposed that this can be avoided through the synthesis of a parallel complementary copy. The logical consequences of this are pursued and developed in a computer simulation, where the behaviour of the parallel copy is compared to the conventional reverse complementary copy. It is found that the parallel copy is more efficient at higher temperatures (up to 90°C). A model for the ribopolymerase, based on the core of the large subunit (LSU) of the ribosome, is described. The geometry of a potential active site for this ribopolymerase suggests that it contained a cavity (now occupied by the aminoacyl-tRNA) and that an amino acid binding in this might have ‘poisoned’ the ribopolymerase by cross-reacting with the nucleoside-triphosphate before polymerization could occur. Based on a similarity to the active site components of the class-I tRNA synthetase enzymes, it is proposed that the amino acid could become attached to the nascent RNA transcript producing a variety of aminoacylated tRNA-like products. Using base-pairing interactions, some of these molecules might cross-link two ribopolymerases, giving rise to a precursor of the modern ribosome. A hybrid dimer, half polymerase and half proto-ribosome, could account for mRNA translocation before the advent of protein elongation factors.

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A Few Experimental Suggestions Using Minerals to Obtain Peptides with a High Concentration of L-Amino Acids and Protein Amino Acids

Symmetry ◽

10.3390/sym12122046 ◽

2020 ◽

Vol 12 (12) ◽

pp. 2046

Author(s):

Dimas A. M. Zaia ◽

Cássia Thaïs B. V. Zaia

Keyword(s):

Amino Acids ◽

Rna World ◽

High Concentration ◽

Protein World ◽

Protein Amino Acids ◽

Hydrothermal Environment ◽

World Hypothesis ◽

Prebiotic Earth ◽

Hydrothermal Environments ◽

Selection Of

The peptides/proteins of all living beings on our planet are mostly made up of 19 L-amino acids and glycine, an achiral amino acid. Arising from endogenous and exogenous sources, the seas of the prebiotic Earth could have contained a huge diversity of biomolecules (including amino acids), and precursors of biomolecules. Thus, how were these amino acids selected from the huge number of available amino acids and other molecules? What were the peptides of prebiotic Earth made up of? How were these peptides synthesized? Minerals have been considered for this task, since they can preconcentrate amino acids from dilute solutions, catalyze their polymerization, and even make the chiral selection of them. However, until now, this problem has only been studied in compartmentalized experiments. There are separate experiments showing that minerals preconcentrate amino acids by adsorption or catalyze their polymerization, or separate L-amino acids from D-amino acids. Based on the [GADV]-protein world hypothesis, as well as the relative abundance of amino acids on prebiotic Earth obtained by Zaia, several experiments are suggested. The main goal of these experiments is to show that using minerals it is possible, at least, to obtain peptides whose composition includes a high quantity of L-amino acids and protein amino acids (PAAs). These experiments should be performed using hydrothermal environments and wet/dry cycles. In addition, for hydrothermal environment experiments, it is very important to use one of the suggested artificial seawaters, and for wet/dry environments, it is important to perform the experiments in distilled water and diluted salt solutions. Finally, from these experiments, we suggest that, without an RNA world or even a pre genetic world, a small peptide set could emerge that better resembles modern proteins.

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RNA Back and Forth: Looking through Ribozyme and Viroid Motifs

Viruses ◽

10.3390/v11030283 ◽

2019 ◽

Vol 11 (3) ◽

pp. 283 ◽

Cited By ~ 5

Author(s):

Marie-Christine Maurel ◽

Fabrice Leclerc ◽

Jacques Vergne ◽

Giuseppe Zaccai

Keyword(s):

Rna World ◽

Hammerhead Ribozyme ◽

Intramolecular Interactions ◽

Modern World ◽

Widespread Occurrence ◽

Living Fossils ◽

Evolution Of Life ◽

Catalytically Active ◽

World Hypothesis ◽

Rna World Hypothesis

Current cellular facts allow us to follow the link from chemical to biochemical metabolites, from the ancient to the modern world. In this context, the “RNA world” hypothesis proposes that early in the evolution of life, the ribozyme was responsible for the storage and transfer of genetic information and for the catalysis of biochemical reactions. Accordingly, the hammerhead ribozyme (HHR) and the hairpin ribozyme belong to a family of endonucleolytic RNAs performing self-cleavage that might occur during replication. Furthermore, regarding the widespread occurrence of HHRs in several genomes of modern organisms (from mammals to small parasites and elsewhere), these small ribozymes have been regarded as living fossils of a primitive RNA world. They fold into 3D structures that generally require long-range intramolecular interactions to adopt the catalytically active conformation under specific physicochemical conditions. By studying viroids as plausible remains of ancient RNA, we recently demonstrated that they replicate in non-specific hosts, emphasizing their adaptability to different environments, which enhanced their survival probability over the ages. All these results exemplify ubiquitous features of life. Those are the structural and functional versatility of small RNAs, ribozymes, and viroids, as well as their diversity and adaptability to various extreme conditions. All these traits must have originated in early life to generate novel RNA populations.

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The “Strong” RNA World Hypothesis: Fifty Years Old

Astrobiology ◽

10.1089/ast.2012.0868 ◽

2013 ◽

Vol 13 (4) ◽

pp. 391-403 ◽

Cited By ~ 93

Author(s):

Marc Neveu ◽

Hyo-Joong Kim ◽

Steven A. Benner

Keyword(s):

Rna World ◽

World Hypothesis ◽

Rna World Hypothesis

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Topological Disentanglement of Linear Polymers under Tension

Polymers ◽

10.3390/polym12112580 ◽

2020 ◽

Vol 12 (11) ◽

pp. 2580

Author(s):

Michele Caraglio ◽

Boris Marcone ◽

Fulvio Baldovin ◽

Enzo Orlandini ◽

Attilio L. Stella

Keyword(s):

Theoretical Description ◽

Contour Length ◽

Topological Invariants ◽

Linear Polymers ◽

Torus Knots ◽

Semiflexible Polymer ◽

Theoretical Predictions ◽

Dynamics Simulations ◽

Remarkable Agreement ◽

Number Of Particles

We develop a theoretical description of the topological disentanglement occurring when torus knots reach the ends of a semiflexible polymer under tension. These include decays into simpler knots and total unknotting. The minimal number of crossings and the minimal knot contour length are the topological invariants playing a key role in the model. The crossings behave as particles diffusing along the chain and the application of appropriate boundary conditions at the ends of the chain accounts for the knot disentanglement. Starting from the number of particles and their positions, suitable rules allow reconstructing the type and location of the knot moving on the chain Our theory is extensively benchmarked with corresponding molecular dynamics simulations and the results show a remarkable agreement between the simulations and the theoretical predictions of the model.

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Solvent viscosity facilitates replication and ribozyme catalysis from an RNA duplex in a model prebiotic process

Nucleic Acids Research ◽

10.1093/nar/gkz496 ◽

2019 ◽

Vol 47 (13) ◽

pp. 6569-6577 ◽

Cited By ~ 4

Author(s):

Christine He ◽

Adriana Lozoya-Colinas ◽

Isaac Gállego ◽

Martha A Grover ◽

Nicholas V Hud

Keyword(s):

Information Transfer ◽

Rna World ◽

Hammerhead Ribozyme ◽

Information Storage ◽

Additional Challenge ◽

The Origin Of Life ◽

World Hypothesis ◽

Synthesis Reactions ◽

Rna World Hypothesis ◽

Single Sequence

Abstract The RNA World hypothesis posits that RNA was once responsible for genetic information storage and catalysis. However, a prebiotic mechanism has yet to be reported for the replication of duplex RNA that could have operated before the emergence of polymerase ribozymes. Previously, we showed that a viscous solvent enables information transfer from one strand of long RNA duplex templates, overcoming ‘the strand inhibition problem'. Here, we demonstrate that the same approach allows simultaneous information transfer from both strands of long duplex templates. An additional challenge for the RNA World is that structured RNAs (like those with catalytic activity) function poorly as templates in model prebiotic RNA synthesis reactions, raising the question of how a single sequence could serve as both a catalyst and as a replication template. Here, we show that a viscous solvent also facilitates the transition of a newly synthesized hammerhead ribozyme sequence from its inactive, duplex state to its active, folded state. These results demonstrate how fluctuating environmental conditions can allow a ribozyme sequence to alternate between acting as a template for replication and functioning as a catalyst, and illustrate the potential for temporally changing environments to enable molecular processes necessary for the origin of life.

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