A continuing frustration for origin of life scientists is that abiotic and, by extension, pre-biotic attempts to develop self-sustaining, evolving molecular systems tend to produce more dead-end substances than macromolecular products with the necessary potential for biostructure and function - the so-called 'tar problem'. Nevertheless primordial life somehow emerged despite that presumed handicap. A resolution of this problem is important in emergence-of-life science because it would provide valuable guidance in choosing subsequent paths of investigation, such as identifying pre-biotic patterns on Mars. To study the problem we set up a simple non-equilibrium flow dynamical model for the coupled temperature and mass dynamics of the decomposition of a polymeric carbohydrate adsorbed on a mineral surface, with incident stochastic thermal fluctuations. Results show that the model system behaves as a reciprocating thermochemical oscillator. The output fluctuation distribution is bimodal, with a right-weighted component that guarantees a bias towards detachment and desorption of monomeric species such as ribose, even while tar is formed concomitantly. This fluctuating thermochemical reciprocator may ensure that non-performing polymers can be fractionated into a refractory carbon reservoir and active monomers which may be reincorporated into better-performing polymers with less vulnerability towards adsorptive tarring.

A primordial environment that hosted complex pre- or proto-biochemical activity would have been subject to random fluctuations. A relevant question is then: What might be the optimum variance of such fluctuations, such that net progress could be made towards a living system? Since lipid-based membrane encapsulation was undoubtedly a key step in chemical evolution, we used a peptide-micelle system in simulated experiments where simple micelles and peptide-stabilized micelles compete for the same amphiphilic lipid substrate. As cyclic thermal driver and energy source we used a thermochemical redox oscillator, to which the micelle reactions are coupled thermally through the activation energies. The long-time series averages taken for increasing values of the fluctuation variance show two distinct minima for simple micelles, but are smoothly increasing for complex micelles. This result suggests that the fluctuation variance is an important parameter in developing and perpetuating complexity. We hypothesize that such an environment may be self-selecting for a complex, evolving chemical system to outcompete simple or parasitic molecular structures.

This chapter discusses a numerical scheme for the solution of the partial differential equations that generalize the classical Lorenz equations, and whether the numerical solution is a meaningful approximation to the corresponding analytic one. It examines numerical solutions to the "spatial" Lorenz equations for a range of parameter values, and discusses the relevance of the results to the behaviour of real systems. The interaction of modes in the spatially varying Lorenz equations, which leads to either stable or unstable solutions, can be investigated in greater detail by examining a simplified model in which only two Fourier modes are present. In conclusion, then it appears that the absence of damping mechanisms for high wavenumber modes, and indeed the fact that the degree of instability grows with wavenumber (leading to a migration of energy from lower to higher modes), means that the Lorenz equations including spatial variation are not a viable model for weakly nonlinear phenomena.

Abstract We consider the numerical solution of competitive exothermic and endothermic reactions in the presence of a chaotic advection flow. The resulting behaviour is characterized by a strong dependence on the competitive reaction history. The burnt temperature is not immediately connected to simple enthalpy calculations, so there is a subtlety in the interplay between the major parameters, notably the Damköhler number, the ratio of the heats of exothermic and endothermic reactions, as well as the ratio of their respective activation energies. This paper seeks to explore the way these parameters affect the steady states of these reaction fronts and their stability.

The hydrogen peroxide (HP) crucible hypothesis proposed here holds that life began in a localized environment on Earth that was perfused with a flow of hydrogen peroxide from a sustained external source, which powered and mediated molecular evolution and the protocellular RNA world. In this article, we consolidate and review recent evidence, both circumstantial and tested in simulation in our work and in the laboratory in others' work, for its multiple roles in the evolution of the first living systems: (1) it provides a periodic power source as the thiosulfate-hydrogen peroxide (THP) redox oscillator, (2) it may act as an agent of molecular change and evolution and mediator of homochirality, and (3) the THP oscillator, subject to Brownian input perturbations, produces a weighted distribution of output thermal fluctuations that favor polymerization and chemical diversification over chemical degradation and simplification. The hypothesis can help to clarify the hero and villain roles of hydrogen peroxide in cell function, and on the singularity of life: of necessity, life evolved early an armory of catalases, the continuing, and all-pervasive presence of which prevents hydrogen peroxide from accumulating anywhere in sufficient quantities to host a second origin. The HP crucible hypothesis is radical, but based on well-known chemistry and physics, it is eminently testable in the laboratory, and many of our simulations provide recipes for such experiments.

An environment far from equilibrium is thought to be a necessary condition for the origin and persistence of life. In this context we report open-flow simulations of a non-enzymic proto-metabolic system, in which hydrogen peroxide acts both as oxidant and driver of thermochemical cycling. We find that a Gaussian perturbed input produces a non-Boltzmann output fluctuation distribution around the mean oscillation maximum. Our main result is that net biosynthesis can occur under fluctuating cyclical but not steady drive. Consequently we may revise the necessary condition to "dynamically far from equilibrium".

In a major extension of previous work, we model the putative hydrothermal rock pore setting for the origin of life on Earth as a series of coupled continuous flow units (the toy train). Perfusing through this train are reactants that set up thermochemical and pH oscillations, and an activated nucleotide that produces monomer and dimer monophosphates. The dynamical equations that model this system are thermally self-consistent. In an innovative step that breaks some new ground, we build stochasticity of the inputs into the model. The computational results infer various constraints and conditions on, and insights into, chemical evolution and the origin of life and its physical setting: long, interconnected porous structures with longitudinal non-uniformity would have been favourable, and the ubiquitous pH dependences of biology may have been established in the prebiotic era. We demonstrate the important role of Gaussian fluctuations of the inputs in driving polymerization, evolution and diversification. In particular, we find that the probability distribution of the resulting output fluctuations is left-skewed and right-weighted (the loaded dice), which could favour chemical evolution towards a living RNA world. We tentatively name this distribution 'Goldilocks'. These results also vindicate the general approach of constructing and running a simple model to learn important new information about a complex system.

It is a remarkable observed fact that all life on Earth is homochiral, its biology using exclusively the D-enantiomer of ribose, the sugar moiety of the ribonucleic acids, and the L-enantiomers of the chiral amino acids. Motivated by concurrent work that elaborates further the role of hydrogen peroxide in providing an oscillatory drive for the RNA world (Ball & Brindley 2015a, J. R. Soc. Interface 12, 20150366, and Ball & Brindley 2015b, this journal, in press), we reappraise the structure and physical properties of this small molecule within this context. Hydrogen peroxide is the smallest, simplest molecule to exist as a pair of non-superimposable mirror images, or enantiomers, a fact which leads us to develop the hypothesis that its enantiospecific interactions with ribonucleic acids led to enantioselective outcomes. We propose a mechanism by which these chiral interactions may have led to amplification of D-ribonucleic acids and extinction of L-ribonucleic acids.

In this paper, we numerically investigate the stability of propagating combustion waves in the competitive exothermic–endothermic reaction model. The analysis is based on the Evans function method and direct numerical integration of the governing partial differential equations. The critical conditions for the onset of instability are found for a broad range of parameter values of the model. It is demonstrated that for the parameter values for which the combustion wave is unstable in the one-step reaction model, the inclusion of the endothermic step can lead to flame stabilization.

It is now accepted that primordial non-cellular RNA communities must have been subject to a periodic drive in order to replicate and prosper. We have proposed the oxidation of thiosulfate by hydrogen peroxide as this drive. This reaction system behaves as (i) a thermochemical and (ii) a pH oscillator, and in this work, we unify (i) and (ii) for the first time. We report thermally self-consistent, dynamical simulations in which the system transitions smoothly from nearly isothermal pH to fully developed thermo-pH oscillatory regimes. We use this oscillator to drive simulated replication of a 39-bp RNA species. Production of replicated duplex under thermo-pH drive was significantly enhanced compared with that under purely thermochemical drive, effectively allowing longer strands to replicate. Longer strands are fitter, with more potential to evolve enzyme activity and resist degradation. We affirm that concern over the alleged toxicity of hydrogen peroxide to life is largely misplaced in the current context, we survey its occurrence in the solar system to motivate its inclusion as a biosignature in the search for life on other worlds and highlight that pH oscillations in a spatially extended, bounded system manifest as the fundamental driving force of life: a proton gradient.

The RNA world of more than 3.7 billion years ago may have drawn on thermal and pH oscillations set up by the oxidation of thiosulfate by hydrogen peroxide (the THP oscillator) as a power source to drive replication. Since this primordial RNA also must have developed enzyme functionalities, in this work we examine the responses of two simple ribozymes to a THP periodic drive, using experimental rate and thermochemical data in a dynamical model for the coupled, self-consistent evolution of all reactants and intermediates. The resulting time traces show that ribozyme performance can be enhanced under pH cycling, and that thermal cycling may have been necessary to achieve large performance gains. We discuss three important ways in which the dynamic hydrogen peroxide medium may have acted as an agent for development of the RNA world towards a cellular world: proton gradients, resolution of the ribozyme versus replication paradox, and vesicle formation.

This paper presents and tests a previously unrecognised mechanism for driving a replicating molecular system on the prebiotic earth. It is proposed that cell-free RNA replication in the primordial soup may have been driven by self-sustained oscillatory thermochemical reactions. To test this hypothesis a well-characterised hydrogen peroxide oscillator was chosen as the driver and complementary RNA strands with known association and melting kinetics were used as the substrate. An open flow system model for the self-consistent, coupled evolution of the temperature and concentrations in a simple autocatalytic scheme is solved numerically, and it is shown that thermochemical cycling drives replication of the RNA strands. For the (justifiably realistic) values of parameters chosen for the simulated example system, the mean amount of replicant produced at steady state is 6.56 times the input amount, given a constant supply of substrate species. The spontaneous onset of sustained thermochemical oscillations via slowly drifting parameters is demonstrated, and a scheme is given for prebiotic production of complementary RNA strands on rock surfaces.

We use a one-dimensional model to present numerical and analytical results on the propagation of combustion waves, driven by competing exothermic and endothermic chemical reactions in parallel with water evaporation. The research was motivated by the phenomenology of emulsion explosives comprising a mixture of fuel and an ammonium nitrate (AN)–water solution. An extensive programme of computational modelling has covered a range of important physical influences, particularly the water fraction and the ambient pressure, on which the endothermic effect of evaporation is critically dependent. A substantial, and not immediately obvious, influence of the evaporation, through its effect on the temperature, is on the fraction of the AN consumed, respectively, by the competing exo- and endothermic reactions, which are controlled by differing, temperature-sensitive kinetics. Self-sustaining travelling combustion waves are initiated for a wide range of parameter values. They are usually oscillatory, regular for small water content and become highly irregular, sometimes causing extinction for larger water content. The numerics are complemented by a brief theoretical analysis, which throws light on the complex and subtle interplay of the two chemical reactions and the evaporation, expressed in the form of a highly convoluted integral over the whole time and space extent of the process.

We consider travelling wave solutions of a reaction–diffusion system corresponding to a single-step homogeneous premixed combustion scheme competitively coupled with an endothermic reaction. Properties of the travelling reaction fronts, such as the wave speed and the burnt temperature are derived numerically over a range of different parameter values, such as those describing the relative enthalpi...

Journal Article Special issue: fluid problems in process engineering Get access Mark Wilson, Mark Wilson University of Leeds Search for other works by this author on: Oxford Academic Google Scholar John Brindley, John Brindley University of Leeds Search for other works by this author on: Oxford Academic Google Scholar Michael Fairweather, Michael Fairweather University of Leeds Search for other works by this author on: Oxford Academic Google Scholar Andy McIntosh, Andy McIntosh University of Leeds Search for other works by this author on: Oxford Academic Google Scholar Gary Sharpe, Gary Sharpe University of Leeds Search for other works by this author on: Oxford Academic Google Scholar Martin Braithwaite, Martin Braithwaite Imperial College London Search for other works by this author on: Oxford Academic Google Scholar Stephen Decent, Stephen Decent University of Birmingham Search for other works by this author on: Oxford Academic Google Scholar David Youdan David Youdan Special Issue: Institute of Mathematics and its Applications Search for other works by this author on: Oxford Academic Google Scholar IMA Journal of Applied Mathematics, Volume 77, Issue 1, February 2012, Page 1, https://doi.org/10.1093/imamat/hxs006 Published: 01 February 2012

In this paper we investigate the properties of the travelling combustion wave solutions in a diffusion-thermal model with a two-step competitive exo–endothermic reaction mechanism in one spatial dimension under adiabatic conditions. The model is analysed both numerically and analytically using asymptotic analysis. It is demonstrated that depending on the parameter values, the flame speed as a function of parameters is either a single-valued monotonic function or a double-valued c-shaped function with the turning point type of behaviour. For the case of single-valued flame speed, two flame regimes are identified: the regime with exo- and endothermic reaction domination. Two different routes to extinction are found as well as regions of the existence of combustion waves in the parameter space. Prospects of further work are also discussed.

We consider the propagation of an exothermic reaction front subject to possible heat loss through a competitive endothermic reaction. Such reaction schemes are of considerable practical importance to industry, where they arise in connection with ammonium nitrate based explosives and explosive gas combustion in underground mines, for example. In particular, competitive endothermic-exothermic reaction schemes are appropriate for the study of the burning of ammonium nitrate (NH4NO3) in the context of emulsion explosives, which finds abundant application in mining and other industries. It is common to represent the chemistry of ammonium nitrate combustion as two competitive reactions one exothermic and one endothermic:NH4NO3 -> NH3 + HNO3 (endothermic)NH4NO3 -> N2O + 2H(2)O (exothermic)Properties of the reaction fronts, which are modelled as travelling wave solutions of a corresponding reaction-diffusion system, are derived numerically over a range of different parameter values, such as those describing the relative enthalpies, rates and activation energies of the endothermic and exothermic reactions. These properties include the speed of the reaction front and the peak temperature produced by the reaction. Unique reaction front solutions have been shown to exist for each distinct combination of the parameter values. The stability of the reaction fronts are of particular interest and it has been shown that when the activation energy of the endothermic reaction is twice that of the exothermic reaction, stable and oscillatory unstable reaction regimes exist. In this case, if the heat released from the exothermic reaction is sufficiently large in proportion to the heat absorbed by the endothermic reaction, the reaction fronts are stable, while if the relative heat released by the exothermic reaction is not sufficiently large the reaction fronts are oscillatory unstable.The analyses presented in the current paper, however, indicate that the assumption of the endothermic activation energy being twice that of the exothermic reaction implies that the endothermic reaction is essentially deactivated. As such, and as shown by Sharples et al. (2011), the behaviour of the reaction front is not all that different to that seen in a single-step exothermic reaction. The analyses reveal a range of parameter values where behaviour of the reaction front could be expected to depart significantly from a single-step exothermic reaction. We present some preliminary numerical results for parameter values in this range and indicate some directions for future work, particularly in regards to the stability of the reaction fronts.

We consider the propagation of a combustion front resulting from the gasless combustion of a condensed state fuel. The propagation of the front, essentially a premixed laminar flame, is supported by an exothermic reaction subject to possible heat loss through a competitive endothermic reaction. The dynamics of the endothermic process inducing the heat loss strongly depend on the temperature and the local fuel concentration. Through an analysis based on high activation energy, the steady-state values of the final burnt temperature as well as the burning velocity are obtained, and the control parameters are identified. Using a linear perturbation method, we assess the stability of the propagating front and obtain a condition for oscillatory behaviour. The critical parameter values for the transition from steady to oscillatory burning speeds are identified. The results represent a generalization of those obtained by Matkowsky and Sivashinsky to include the effects of heat loss induced by a competitive endothermic reaction.