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Non-equilibrium selection pressures were proposed for the formation of oligonucleotides with rich functionalities encoded in their sequences, such as catalysis. Since phase separation was shown to direct various chemical processes, we ask whether condensed phases can provide mechanisms for sequence selection. To answer this question, we use non-equilibrium thermodynamics and describe the reversible oligomerization of different monomers to sequences at non-dilute conditions prone to phase separation. We find that when sequences oligomerize, their interactions give rise to phase separation, boosting specific sequences' enrichment and depletion. Our key result is that phase separation gives rise to a selection pressure for the oligomerization of specific sequence patterns when fragmentation maintains the system away from equilibrium. Specifically, slow fragmentation favors alternating sequences that interact well with their environment (more cooperative), while fast fragmentation selects sequences with extended motifs capable of specific sequence interactions (less cooperative). Our results highlight that out-of-equilibrium condensed phases could provide versatile hubs for Darwinian-like evolution toward functional sequences, both relevant for the molecular origin of life and de novo life.

We calculate the thermophoretic drift of a charged single colloidal particle with hydrodynamically slipping surface immersed in an electrolyte solution in response to a small temperature gradient. Here, we rely on a linearized hydrodynamic approach for the fluid flow and the motion of the electrolyte ions while keeping the full nonlinearity of the Poisson-Boltzmann equation of the unperturbed system to account for possible large surface charging. The partial differential equations are transformed into a coupled set of ordinary differential equations in linear response. Numerical solutions are elaborated for parameter regimes of small and large Debye shielding and different hydrodynamic boundary conditions encoded in a varying slip length. Our results are in good agreement with predictions from recent theoretical work and successfully describe experimental observations on thermophoresis of DNA. We also compare our numerical results with experimental data on polystyrene beads., Comment: 24 pages with 7 figures

Alkaline vents (AV) are hypothesized to have been a setting for the emergence of life, by creating strong gradients across inorganic membranes within chimney structures. In the past, 3-dimensional chimney structures were formed under laboratory conditions, however, no in situ visualisation or testing of the gradients was possible. We develop a quasi-2-dimensional microfluidic model of alkaline vents that allows spatio-temporal visualisation of mineral precipitation in low volume experiments. Upon injection of an alkaline fluid into an acidic, iron-rich solution, we observe a diverse set of precipitation morphologies, mainly controlled by flow-rate and ion-concentration. Using microscope imaging and pH dependent dyes, we show that finger-like precipitates can facilitate formation and maintenance of microscale pH gradients and accumulation of dispersed particles in confined geometries. Our findings establish a model to investigate the potential of gradients across a semi-permeable boundary for early compartmentalisation, accumulation and chemical reactions at the origins of life., Comment: 13 pages, 4 figures

Free-floating planets (FFPs) can result from dynamical scattering processes happening in the first few million years of a planetary system's life. Several models predict the possibility, for these isolated planetary-mass objects, to retain exomoons after their ejection. The tidal heating mechanism and the presence of an atmosphere with a relatively high optical thickness may support the formation and maintenance of oceans of liquid water on the surface of these satellites. In order to study the timescales over which liquid water can be maintained, we perform dynamical simulations of the ejection process and infer the resulting statistics of the population of surviving exomoons around free-floating planets. The subsequent tidal evolution of the moons' orbital parameters is a pivotal step to determine when the orbits will circularize, with a consequential decay of the tidal heating. We find that close-in ($a \lesssim 25 $R$_{\rm J}$) Earth-mass moons with CO$_2$-dominated atmospheres could retain liquid water on their surfaces for long timescales, depending on the mass of the atmospheric envelope and the surface pressure assumed. Massive atmospheres are needed to trap the heat produced by tidal friction that makes these moons habitable. For Earth-like pressure conditions ($p_0$ = 1 bar), satellites could sustain liquid water on their surfaces up to 52 Myr. For higher surface pressures (10 and 100 bar), moons could be habitable up to 276 Myr and 1.6 Gyr, respectively. Close-in satellites experience habitable conditions for long timescales, and during the ejection of the FFP remain bound with the escaping planet, being less affected by the close encounter., Comment: 21 pages, 12 figures, accepted for publication on International Journal of Astrobiology

Mechanisms of nucleic acid accumulation were likely critical to the emergence of life in the ferruginous oceans of the early Earth. How exactly prebiotic geological settings accumulated nucleic acids from dilute aqueous solutions, is poorly understood. As a possible solution to this concentration problem, we simulated the conditions of prebiotic low-temperature alkaline hydrothermal vents in co-precipitation experiments to investigate the potential of ferruginous chemical gardens to accumulate nucleic acids via sorption. The injection of an alkaline solution into an artificial ferruginous solution under anoxic conditions (O2 <0.01% of present atmospheric levels) and at ambient temperatures, caused the precipitation of amakinite (white rust), which quickly converted to chloride-containing fougerite (green rust). RNA was only extractable from the ferruginous solution in the presence of a phosphate buffer, suggesting RNA in solution was bound to Fe2+ ions. During chimney formation, this iron-bound RNA rapidly accumulated in the white and green rust chimney structure, as it was depleted from the surrounding solution. Our findings reveal that in the oceans of the early Earth, white and green rust chimneys were likely key geochemical features that can rapidly sequester and accumulate RNA. This represents a new mechanism for nucleic acid accumulation, in addition to wet dry cycles, and may have promoted RNA survival in a dilute prebiotic ocean.

The emergence of functional oligonucleotides on early Earth required a molecular selection mechanism to screen for specific sequences with prebiotic functions. Cyclic processes such as daily temperature oscillations were ubiquitous in this environment and could trigger oligonucleotide phase separation. Here, we propose sequence selection based on phase separation cycles realized through sedimentation in a system subjected to the feeding of oligonucleotides. Using theory and experiments with DNA, we show sequence-specific enrichment in the sedimented dense phase, in particular of short 22-mer DNA sequences. The underlying mechanism selects for complementarity, as it enriches sequences that tightly interact in the condensed phase through base-pairing. Our mechanism also enables initially weakly biased pools to enhance their sequence bias or to replace the most abundant sequences as the cycles progress. Our findings provide an example of a selection mechanism that may have eased screening for the first auto-catalytic self-replicating oligonucleotides.

Non-equilibrium conditions must have been crucial for the assembly of the first informational polymers of early life, but supporting their formation and continuous enrichment in a long-lasting environment. Here, we explore how gas bubbles in water subjected to a thermal gradient, a likely scenario within crustal mafic rocks on the early Earth, drive a complex, continuous enrichment of prebiotic molecules. NRA precursors, monomers, active ribozymes, oligonucleotides and lipids are shown to (1) cycle between dry and wet states, enabling the central step of RNA phosphorylation, (2) accumulate at the gas-water interface to drastically increase ribozymatic activity, (3) condense into hydrogels, (4) form pure crystals and (5) encapsulate into protecting vesicle aggregates that subsequently undergo fission. These effects occur within less than 30 min. The findings unite, in one location, the physical conditions that were crucial for the chemical emergence of biopolymers. They suggest that heated microbubbles could have hosted the first cycles of molecular evolution., Comment: 27 pages, 7 Figures

The emergence of longer information-carrying and functional nucleotide polymers from random short strands was a major stepping stone at the dawn of life. But the formation of those polymers under temperature oscillation required some form of selection. A plausible mechanism is template-based ligation where theoretical work already suggested a reduction in information entropy. Here, we show how nontrivial sequence patterns emerge in a system of random 12mer DNA sequences subject to enzyme-based templated ligation reaction and temperature cycling. The strands acted both as a template and substrates of the reaction and thereby formed longer oligomers. The selection for templating sequences leads to the development of a multiscale ligation landscape. A position-dependent sequence pattern emerged with a segregation into mutually complementary pools of A-rich and T-rich sequences. Even without selection for function, the base pairing of DNA with ligation showed a dynamics resembling Darwinian evolution., Comment: 11 pages, 5 figures, SI attached

Each living species carries a complex DNA sequence that determines their unique features and functionalities. It is generally assumed that life started from a random pool of oligonucleotides sequences, generated by a prebiotic polymerization of nucleotides. The mechanism that initially facilitated the emergence of sequences that code for the function of the first species from such a random pool of sequences remains unknown. It is a central problem of the origin of life. An interesting option would be a self-selection mechanism by spontaneous symmetry breaking. Initial concentration fluctuations of specific sequence motifs would have been amplified and outcompeted less abundant sequences, enhancing the signal to noise to replicate and select functional sequences. Here, we demonstrate with experimental and theoretical findings that templated ligation would provide such a self-selection. In templated ligation, two adjacent single sequences strands are chemically joined when a third complementary strand sequence brought them in close proximity. This simple mechanism was a likely side-product of a prebiotic polymerization chemistry once the strands reach the length to form double stranded species. As shown here, the ligation gave rise to a nonlinear replication process by the cooperative ligation of matching sequences which self-promoted their own elongation. This led to a cascade of enhanced template binding and faster ligation reactions. A requirement was the reshuffling of the strands by thermal cycling, enabled for example by microscale convection. Assuming that templated ligation was driven by the same chemical mechanism that generated prebiotic polymerization of oligonucleotides, the mechanism could function as a missing link between polymerization and the self-stabilized replication, offering a pathway to the autonomous emergence of Darwinian evolution for the origin of life., Comment: 36 pages, 18 figures

The thermal expansion of a fluid combined with a temperature-dependent viscosity introduces nonlinearities in the Navier-Stokes equations unrelated to the convective momentum current. The couplings generate the possibility for net fluid flow at the microscale controlled by external heating. This novel thermo-mechanical effect is investigated for a thin fluid chamber by a numerical solution of the Navier-Stokes equations and analytically by a perturbation expansion. A demonstration experiment confirms the basic mechanism and quantitatively validates our theoretical analysis., Comment: 5 pages, 3 figures, accepted by Physical Review Letters

Thermophoresis (thermodiffusion, Soret effect) moves molecules along thermal gradients. We measure its phenomenological linear drift relation by single particle tracking in convection-free settings. For moderate thermal gradients, drift velocity depends linearly on the gradient. However, for strong thermal gradients, we find a nonlinear dependence of the drift on the applied gradient for large Soret coefficient and particle radius. Interestingly, the onset of the nonlinearity coincides with a local disequilibrium of the particle. Nonlinear thermophoresis resolves several fundamental contradictions between thermophoretic experiments and theory., Comment: 9 pages, 4 Figures

Thermophoresis moves molecules along temperature gradients, typically from hot to cold. We superpose fluid flow with thermophoretic molecule flow under well defined microfluidic conditions, imaged by fluorescence microscopy. DNA is trapped and accumulated 16-fold in regions where both flows move in opposite directions. Strong 800-fold accumulation is expected, however with slow trapping kinetics. The experiment is equally described by a three-dimensional and one-dimensional analytical model. As an application, we show how a radially converging temperature field confines short DNA into a 10 um small spot., Comment: 9 pages, 6 figures

We analyze wealth condensation for a wide class of stochastic economy models on the basis of the economic analog of thermodynamic potentials, termed transfer potentials. The economy model is based on three common transfers modes of wealth: random transfer, profit proportional to wealth and motivation of poor agents to work harder. The economies never reach steady state. Wealth condensation is the result of stochastic tunneling through a metastable transfer potential. In accordance with reality, both wealth and income distribution transiently show Pareto tails for high income subjects. For metastable transfer potentials, exponential wealth condensation is a robust feature. For example with 10 % annual profit 1% of the population owns 50 % of the wealth after 50 years. The time to reach such a strong wealth condensation is a hyperbolic function of the annual profit rate., Comment: 8 pages, 8 figures

We analyze a monetary system of random money transfer on the basis of double entry bookkeeping. Without boundary conditions, we do not reach a price equilibrium and violate text-book formulas of economists quantity theory (MV=PQ). To match the resulting quantity of money with the model assumption of a constant price, we have to impose boundary conditions. They either restrict specific transfers globally or impose transfers locally. Both connect through a general framework of transfer potentials. We show that either restricted or imposed transfers can shape gaussian, tent-shape exponential, boltzmann-exponential, pareto or periodic equilibrium distributions. We derive the master equation and find its general time dependent approximate solution. An equivalent of quantity theory for random money transfer under the boundary conditions of transfer potentials is given., Comment: 15 pages, 2 figures