Information, Coding, and Biological Function: The Dynamics of Life

In the mid-20th century, two new scientific disciplines emerged forcefully: molecular biology and information-communication theory. At the beginning, cross-fertilization was so deep that the term genetic code was universally accepted for describing the meaning of triplets of mRNA (codons) as amino acids. However, today, such synergy has not taken advantage of the vertiginous advances in the two disciplines and presents more challenges than answers. These challenges not only are of great theoretical relevance but also represent unavoidable milestones for next-generation biology: from personalized genetic therapy and diagnosis to Artificial Life to the production of biologically active proteins. Moreover, the matter is intimately connected to a paradigm shift needed in theoretical biology, pioneered a long time ago, that requires combined contributions from disciplines well beyond the biological realm. The use of information as a conceptual metaphor needs to be turned into quantitative and predictive models that can be tested empirically and integrated in a unified view. Successfully achieving these tasks requires a wide multidisciplinary approach, including Artificial Life researchers, to address such an endeavour.

A microfluidic labyrinth self-assembled by a chemical garden

Chemical gardens, self-assembling precipitates that spontaneously form when a metal salt is added to a solution of another precipitating anion, are of interest for various applications including producing reactive materials in controlled structures. Here, we report on two chemical garden reaction systems (CuCl2 and Cu(NO3)2 seed crystals submerged in sodium silicate) that produced self-assembled microfluidic labyrinths in a vertical 2D Hele-Shaw reactor. The formation of labyrinths as well as the specific growth modes of the precipitate were dependent on the silicate concentration: CuCl2 labyrinths formed only at 3 and 4 M silicate and Cu(NO3)2 labyrinths formed only at 4 and 5 M silicate. The labyrinth structures contained silicate on the exterior and crystalline material interpreted as hydrated minerals from the metal salt in their interiors. The bubble-guided tubes that form labyrinths can be controlled by changing the angle of the 2D reaction cell; this suggests that future experiments of this type could form self-organizing structures with controlled composition and orientation for use in microfluidics and various materials science applications.

Hybrid organic-inorganic structures trigger the formation of primitive cell-like compartments

Alkaline hydrothermal vents have become a candidate setting for the origins of life on Earth and beyond. This is due to several key features including the presence of gradients of temperature, redox potential, pH, the availability of inorganic minerals, and the existence of a network of inorganic pore spaces that could have served as primitive compartments. Chemical gardens have long been used as experimental proxies for hydrothermal vents. This paper investigates-10pc]Please note that the spelling of the following author name in the manuscript differs from the spelling provided in the article metadata: Richard J. G. Löffler. The spelling provided in the manuscript has been retained; please confirm. a set of prebiotic interactions between such inorganic structures and fatty alcohols. The integration of a medium-chain fatty alcohol, decanol, within these inorganic minerals, produced a range of emergent 3 dimensions structures at both macroscopic and microscopic scales. Fatty alcohols can be considered plausible prebiotic amphiphiles that might have assisted the formation of protocellular structures such as vesicles. The experiments presented herein show that neither chemical gardens nor decanol alone promote vesicle formation, but chemical gardens grown in the presence of decanol, which is then integrated into inorganic mineral structures, support vesicle formation. These observations suggest that the interaction of fatty alcohols and inorganic mineral structures could have played an important role in the emergence of protocells, yielding support for the evolution of living cells.

Quantum noise may limit the mechanosensory sensitivity of cilia in the left-right organizer of the vertebrate bodyplan

Could nature be harnessing quantum mechanics in cilia to optimize the sensitivity of the mechanism of left-right symmetry breaking during development in vertebrates? I evaluate whether mechanosensing - i.e., the detection of a left-right asymmetric signal through mechanical stimulation of sensory cilia, as opposed to biochemical signalling - might be functioning in the embryonic left-right organizer of the vertebrate bodyplan through quantum mechanics. I conclude that there is a possible role for quantum biology in mechanosensing in cilia. The system may not be limited by classical thermal noise, but instead by quantum noise, with an amplification process providing active cooling.

The Effect of the Presence of Amino Acids on the Precipitation of Inorganic Chemical-Garden Membranes: Biomineralization at the Origin of Life

If life developed in hydrothermal vents, it would have been within mineral membranes. The first proto-cells must have evolved to manipulate the mineral membranes that formed their compartments in order to control their metabolism. There must have occurred a biological takeover of the self-assembled mineral structures of the vents, with the incorporation of proto-biological molecules within the mineral membranes to alter their properties for life's purposes. Here, we study a laboratory analogue of this process: chemical-garden precipitation of the amino acids arginine and tryptophan with the metal salt iron chloride and sodium silicate. We produced these chemical gardens using different methodologies in order to determine the dependence of the morphology and chemistry on the growth conditions, as well as the effect of the amino acids on the formation of the iron-silicate chemical garden. We compared the effects of having amino acids initially within the forming chemical garden, corresponding to the internal zones of hydrothermal vents, or else outside, corresponding to the surrounding ocean. The characterization of the formed chemical gardens using X-ray diffraction, Fourier transform infrared spectroscopy, elemental analysis, and scanning electron microscopy demonstrates the presence of amino acids in these structures. The growth method in which the amino acid is initially in the tablet with the iron salt is that which generated chemical gardens with more amino acids in their structures.

Downward fingering accompanies upward tube growth in a chemical garden grown in a vertical confined geometry

Chemical gardens are self-assembled structures of mineral precipitates enabled by semi-permeable membranes. To explore the effects of gravity on the formation of chemical gardens, we have studied chemical gardens grown from cobalt chloride pellets and aqueous sodium silicate solution in a vertical Hele-Shaw cell. Through photography, we have observed and quantitatively analysed upward growing tubes and downward growing fingers. The latter were not seen in previous experimental studies involving similar physicochemical systems in 3-dimensional or horizontal confined geometry. To better understand the results, further studies of flow patterns, buoyancy forces, and growth dynamics under schlieren optics have been carried out, together with characterisation of the precipitates with scanning electron microscopy and X-ray diffractometry. In addition to an ascending flow and the resulting precipitation of tubular filaments, a previously not reported descending flow has been observed which, under some conditions, is accompanied by precipitation of solid fingering structures. We conclude that the physics of both the ascending and descending flows are shaped by buoyancy, together with osmosis and chemical reaction. The existence of the descending flow might highlight a limitation in current experimental methods for growing chemical gardens under gravity, where seeds are typically not suspended in the middle of the solution and are confined by the bottom of the vessel.

Self-Assembled Structures Formed in CO2-Enriched Atmospheres: A Case-Study for Martian Biomimetic Forms

The aim of this study was to investigate the biomimetic precipitation processes that follow the chemical-garden reaction of brines of CaCl₂ and sulfate salts with silicate in alkaline conditions under a Mars-type CO₂-rich atmosphere. We characterize the precipitates with environmental scanning electron microscope micrography, micro-Raman spectroscopy, and X-ray diffractometry. Our analysis results indicate that self-assembled carbonate structures formed with calcium chloride can have vesicular and filamentary features. With magnesium sulfate as a reactant a tentative assignment with Raman spectroscopy indicates the presence of natroxalate in the precipitate. These morphologies and compounds appear through rapid sequestration of atmospheric CO₂ by alkaline solutions of silica and salts.

Archimedean Spirals Form at Low Flow Rates in Confined Chemical Gardens

We describe and study the formation of confined chemical garden patterns. At low flow rates of injection of cobalt chloride solution into a Hele-Shaw cell filled with sodium silicate, the precipitate forms with a thin filament wrapping around an expanding "candy floss" structure. The result is the formation of an Archimedean spiral structure. We model the growth of the structure mathematically. We estimate the effective density of the precipitate and calculate the membrane permeability. We set the results within the context of recent experimental and modeling work on confined chemical garden filaments.

Filament dynamics in vertical confined chemical gardens

When confined to a Hele-Shaw cell, chemical gardens can grow as filaments, narrow structures with an erratic and tortuous trajectory. In this work, the methodology applied to studies with horizontal Hele-Shaw cells is adapted to a vertical configuration, thus introducing the effect of buoyancy into the system. The motion of a single filament tip is modeled by taking into account its internal pressure and the variation of the concentration of precipitate that constitutes the chemical garden membrane. While the model shows good agreement with the results, it also suggests that the concentration of the host solution of sodium silicate also plays a role in the growth of the structures despite being in stoichiometric excess.

Non-power positional number representation systems, bijective numeration, and the Mesoamerican discovery of zero

Pre-Columbian Mesoamerica was a fertile crescent for the development of number systems. A form of vigesimal system seems to have been present from the first Olmec civilization onwards, to which succeeding peoples made contributions. We discuss the Maya use of the representational redundancy present in their Long Count calendar, a non-power positional number representation system with multipliers 1, 20, 18 × 20, …, 18 × 20ⁿ. We demonstrate that the Mesoamericans did not need to invent positional notation and discover zero at the same time because they were not afraid of using a number system in which the same number can be written in different ways. A Long Count number system with digits from 0 to 20 is seen later to pass to one using digits 0 to 19, which leads us to propose that even earlier there may have been an initial zeroless bijective numeration system whose digits ran from 1 to 20. Mesoamerica was able to make this conceptual leap to the concept of a cardinal zero to perform arithmetic owing to a familiarity with multiple and redundant number representation systems.

Filament dynamics in planar chemical gardens

Filaments in a planar chemical garden grow following tortuous, erratic paths. We show from statistical mechanics that this scaling results from a self-organized dispersion mechanism. Effective diffusivities as high as 10-5 m2 s-1 are measured in 2D laboratory experiments. This efficient transport is four orders of magnitude larger than molecular diffusion in a liquid, and ensures widespread contact and exchange between fluids in the chemical-garden structure and its surrounding environment.

Stokes' law, viscometry, and the Stokes falling sphere clock

Clocks run through the history of physics. Galileo conceived of using the pendulum as a timing device on watching a hanging lamp swing in Pisa cathedral; Huygens invented the pendulum clock; and Einstein thought about clock synchronization in his Gedankenexperiment that led to relativity. Stokes derived his law in the course of investigations to determine the effect of a fluid medium on the swing of a pendulum. I sketch the work that has come out of this, Stokes drag, one of his most famous results. And to celebrate the 200th anniversary of George Gabriel Stokes' birth I propose using the time of fall of a sphere through a fluid for a sculptural clock-a public kinetic artwork that will tell the time. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Stokes at 200 (part 2)

We present the second half of the papers from the Stokes²⁰⁰ symposium celebrating the bicentenary of George Gabriel Stokes. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Geometric mixing

Mixing fluids often involves a periodic action, like stirring one's tea. But reciprocating motions in fluids at low Reynolds number, in Stokes flows where inertia is negligible, lead to periodic cycles of mixing and unmixing, because the physics, molecular diffusion excepted, is time reversible. So how can fluid be mixed in such circumstances? The answer involves a geometric phase. Geometric phases are found everywhere in physics as anholonomies, where after a closed circuit in the parameters, some system variables do not return to their original values. We discuss the geometric phase in fluid mixing: geometric mixing. This article is part of the theme issue 'Stokes at 200 (part 2)'.

The fluid mechanics of poohsticks

The year 2019 marked the bicentenary of George Gabriel Stokes, who in 1851 described the drag-Stokes drag-on a body moving immersed in a fluid, and 2020 is the centenary of Christopher Robin Milne, for whom the game of poohsticks was invented; his father A. A. Milne's The House at Pooh Corner, in which it was first described in print, appeared in 1928. So this is an apt moment to review the state of the art of the fluid mechanics of a solid body in a complex fluid flow, and one floating at the interface between two fluids in motion. Poohsticks pertains to the latter category, when the two fluids are water and air. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Nacre Is a Liquid-Crystal Thermometer of the Oceans

Nacre, or mother of pearl, is a biomaterial with a layered structure. In a recent geological study, researchers found that the width of the nacre layers depends on the formation temperature, which is determined by the ocean water temperature. A linear dependence of layer width with respect to temperature is understandable within the transient liquid-crystalline nature of incipient nacre. Thus, developing nacre is a liquid-crystal thermometer recording its formation temperature. A more complete understanding of nacre formation is of interest not only for biology and geology, in terms of biomineralization and paleoclimatology, but also for materials science: for reproducing nacre or fabricating synthetic analogues and also potentially for developing new classes of layered materials with layer spacings tunable by pH and temperature.

The bee Tetragonula builds its comb like a crystal

Stingless bees of the genus Tetragonula construct a brood comb with a spiral or a target pattern architecture in three dimensions. Crystals possess these same patterns on the molecular scale. Here, we show that the same excitable-medium dynamics governs both crystal nucleation and growth and comb construction in Tetragonula, so that a minimal coupled-map lattice model based on crystal growth explains how these bees produce the structures seen in their bee combs.

Stokes at 200: a celebration of the remarkable achievements of Sir George Gabriel Stokes two hundred years after his birth

Sir George Gabriel Stokes PRS was for 30 years an inimitable Secretary of the Royal Society and its President from 1885 to 1890. Two hundred years after his birth, Stokes is a towering figure in physics and applied mathematics; fluids, asymptotics, optics, acoustics among many other fields. At the Stokes²⁰⁰ meeting, held at Pembroke College, Cambridge from 15-18th September 2019, an invited audience of about 100 discussed the state of the art in all the modern research fields that have sprung from his work in physics and mathematics, along with the history of how we have got from Stokes' contributions to where we are now. This theme issue is based on work presented at the Stokes²⁰⁰ meeting. In bringing together people whose work today is based upon Stokes' own, we aim to emphasize his influence and legacy at 200 to the community as a whole. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Nonlinear dynamics determines the thermodynamic instability of condensed matter in vacuo

Condensed matter is thermodynamically unstable in a vacuum. That is what thermodynamics tells us through the relation showing that condensed matter at temperatures above absolute zero always has non-zero vapour pressure. This instability implies that at low temperatures energy must not be distributed equally among atoms in the crystal lattice but must be concentrated. In dynamical systems such concentrations of energy in localized excitations are well known in the form of discrete breathers, solitons and related nonlinear phenomena. It follows that to satisfy thermodynamics such localized excitations must exist in systems of condensed matter at arbitrarily low temperature and as such the nonlinear dynamics of condensed matter is crucial for its thermodynamics. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Stokes, Tyndall, Ruskin and the nineteenth-century beginnings of climate science

Although we humans have known since the first smokey campfires of prehistory that our activities might alter our local surroundings, the nineteenth century saw the first indications that humankind might alter the global environment; what we currently know as anthropogenic climate change. We are now celebrating the bicentenaries of three figures with a hand in the birth of climate science. George Stokes, John Tyndall and John Ruskin were born in August 1819, August 1820 and February 1819, respectively. We look back from the perspective of two centuries following their births. We outline their contributions to climate science: understanding the equations of fluid motion and the recognition of the need to collect global weather data together with comprehending the role in regulating terrestrial temperature played by gases in the atmosphere. This knowledge was accompanied by fears of the Earth's regression to another ice age, together with others that industrialization was ruining humankind's health, morals and creativity. The former fears of global cooling were justified but seem strange now that the balance has tipped so far the other way towards global warming; the latter, on the other hand, today seem very prescient. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Chaos and periodicities in a climatic time series of the Iberian Margin

We analyze the time series of the temperature of the sedimentary core MD01-2443 originating from the Iberian Margin with a duration of 420 kyr. The series has been tested for unit-root and a long term trend is estimated. We identify four significant periodicities together with a low climatic activity every 100 kyr, and these were associated with internal and external forcings. Also, we identify a high-frequency fast component that acts on top of a nonlinear, irreversible slow-changing dynamics. We find the presence of chaos in the climate of the Iberian Margin by means of a neural network asymptotic test on the largest Lyapunov exponent. The analysis suggests that the chaotic dynamics is associated with the fast high-frequency component. We also carry out a statistical analysis of the dimensionality of the attractor. Our results confirm the possibility that periodic behavior and chaos may coexist on different time scales. This could lead to different degrees of predictability in the climate system according to the characteristic time scales and/or phase-space locations.

Chemobrionics: From Self-Assembled Material Architectures to the Origin of Life

Self-organizing precipitation processes, such as chemical gardens forming biomimetic micro- and nanotubular forms, have the potential to show us new fundamental science to explore, quantify, and understand nonequilibrium physicochemical systems, and shed light on the conditions for life's emergence. The physics and chemistry of these phenomena, due to the assembly of material architectures under a flux of ions, and their exploitation in applications, have recently been termed chemobrionics. Advances in understanding in this area require a combination of expertise in physics, chemistry, mathematical modeling, biology, and nanoengineering, as well as in complex systems and nonlinear and materials sciences, giving rise to this new synergistic discipline of chemobrionics.

Chemosensing versus mechanosensing in nodal and Kupffer's vesicle cilia and in other left-right organizer organs

How is sensing carried out by cilia in the mouse node, zebrafish Kupffer's vesicle and similar left-right (LR) organizer organs in other species? Two possibilities have been put forward. In the former, cilia would detect some chemical species in the fluid; in the latter, they would detect fluid flow. In either case, the hypothesis is that an imbalance would be detected between this signalling coming from cilia on the left and right sides of the organizer, which would initiate a cascade of signals leading ultimately to the breaking of LR symmetry in the developing body plan of the organism. We review the evidence for both hypotheses. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.

Intrinsic concentration cycles and high ion fluxes in self-assembled precipitate membranes

Concentration cycles are important for bonding of basic molecular building components at the emergence of life. We demonstrate that oscillations occur intrinsically in precipitation reactions when coupled with fluid mechanics in self-assembled precipitate membranes, such as at submarine hydrothermal vents. We show that, moreover, the flow of ions across one pore in such a prebiotic membrane is larger than that across one ion channel in a modern biological cell membrane, suggesting that proto-biological processes could be sustained by osmotic flow in a less efficient prebiotic environment. Oscillations in nanoreactors at hydrothermal vents may be just right for these warm little pores to be the cradle of life.

Self-Assembling Ice Membranes on Europa: Brinicle Properties, Field Examples, and Possible Energetic Systems in Icy Ocean Worlds

Brinicles are self-assembling tubular ice membrane structures, centimeters to meters in length, found beneath sea ice in the polar regions of Earth. We discuss how the properties of brinicles make them of possible importance for chemistry in cold environments-including that of life's emergence-and we consider their formation in icy ocean worlds. We argue that the non-ice composition of the ice on Europa and Enceladus will vary spatially due to thermodynamic and mechanical properties that serve to separate and fractionate brines and solid materials. The specifics of the composition and dynamics of both the ice and the ocean in these worlds remain poorly constrained. We demonstrate through calculations using FREZCHEM that sulfate likely fractionates out of accreting ice in Europa and Enceladus, and thus that an exogenous origin of sulfate observed on Europa's surface need not preclude additional endogenous sulfate in Europa's ocean. We suggest that, like hydrothermal vents on Earth, brinicles in icy ocean worlds constitute ideal places where ecosystems of organisms might be found.

Exploding Chemical Gardens: A Phase-Change Clock Reaction

Chemical gardens and clock reactions are two of the best-known demonstration reactions in chemistry. Until now these have been separate categories. We have discovered that a chemical garden confined to two dimensions is a clock reaction involving a phase change, so that after a reproducible and controllable induction period it explodes.

Filiform corrosion as a pressure-driven delamination process

Filiform corrosion produces long and narrow trails on various coated metals through the detachment of the coating layer from the substrate. In this work, we present a combined experimental and theoretical analysis of this process with the aim to describe quantitatively the shape of the cross-section, perpendicular to the direction of propagation, of the filaments produced. For this purpose, we introduce a delamination model of filiform corrosion dynamics and show its compatibility with experimental data where the coating thickness has been varied systematically.

Filament dynamics in confined chemical gardens and in filiform corrosion

Once rescaled by the preferred wavenumber ω* of the curvature power spectrum, both filiform corrosion and chemical garden filaments display similar dynamics.

On the differing growth mechanisms of black-smoker and Lost City-type hydrothermal vents

Black smokers and Lost City-type springs are varieties of hydrothermal vents on the ocean floors that emit hot, acidic water and cool, alkaline water, respectively. While both produce precipitation structures as the issuing fluid encounters oceanic water, Lost City-type hydrothermal vents in particular have been implicated in the origin of life on the Earth. We present a parallel-velocity flow model for the radius and flow rate of a cylindrical jet of fluid that forms the template for the growth of a tube precipitated about itself and we compare the solution with previous laboratory experimental results from growth of silicate chemical gardens. We show that when the growth of the solid structure is determined by thermal diffusion, fluid flow is slow at the solid-liquid contact. However, in the case of chemical diffusive transport, the fluid jet effectively drags the liquid in the pores of the solid precipitate. These findings suggest a continuum in the diffusive growth rate of hydrothermal vent structures, where Lost City-type hydrothermal vents favour contact between the vent fluid and the external seawater. We explore the implications for the road to life.

Organic membranes determine the pattern of the columnar prismatic layer of mollusc shells

The degree to which biological control is exercised compared to physical control of the organization of biogenic materials is a central theme in biomineralization. We show that the outlines of biogenic calcite domains with organic membranes are always of simple geometries, while without they are much more complex. Moreover, the mineral prisms enclosed within the organic membranes are frequently polycrystalline. In the prismatic layer of the mollusc shell, organic membranes display a dynamics in accordance with the von Neumann-Mullins and Lewis Laws for two-dimensional foam, emulsion and grain growth. Taken together with the facts that we found instances in which the crystals do not obey such laws, and that the same organic membrane pattern can be found even without the mineral infilling, our work indicates that it is the membranes, not the mineral prisms, that control the pattern, and the mineral enclosed within the organic membranes passively adjusts to the dynamics dictated by the latter.

Self-assembling iron oxyhydroxide/oxide tubular structures: laboratory-grown and field examples from Rio Tinto

Rio Tinto in southern Spain has become of increasing astrobiological significance, in particular for its similarity to environments on early Mars. We present evidence of tubular structures from sampled terraces in the stream bed at the source of the river, as well as ancient, now dry, terraces. This is the first reported finding of tubular structures in this particular environment. We propose that some of these structures could be formed through self-assembly via an abiotic mechanism involving templated precipitation around a fluid jet, a similar mechanism to that commonly found in so-called chemical gardens. Laboratory experiments simulating the formation of self-assembling iron oxyhydroxide tubes via chemical garden/chemobrionic processes form similar structures. Fluid-mechanical scaling analysis demonstrates that the proposed mechanism is plausible. Although the formation of tube structures is not itself a biosignature, the iron mineral oxidation gradients across the tube walls in laboratory and field examples may yield information about energy gradients and potentially habitable environments.

Increased methane emissions from deep osmotic and buoyant convection beneath submarine seeps as climate warms

High speeds have been measured at seep and mud-volcano sites expelling methane-rich fluids from the seabed. Thermal or solute-driven convection alone cannot explain such high velocities in low-permeability sediments. Here we demonstrate that in addition to buoyancy, osmotic effects generated by the adsorption of methane onto the sediments can create large overpressures, capable of recirculating seawater from the seafloor to depth in the sediment layer, then expelling it upwards at rates of up to a few hundreds of metres per year. In the presence of global warming, such deep recirculation of seawater can accelerate the melting of methane hydrates at depth from timescales of millennia to just decades, and can drastically increase the rate of release of methane into the hydrosphere and perhaps the atmosphere.

Large methane hydrates reserves are found in mud volcanoes, but climate change may lead to methane release. Here, the authors show that methane adsorption creates overpressures leading to rapid recirculation of seawater, thus reducing the melting timescales of methane hydrates from millennia to decades.

Fluid-flow-templated self-assembly of calcium carbonate tubes in the laboratory and in biomineralization: The tubules of the watering-pot shells, Clavagelloidea

We show with laboratory experiments that self-assembled mineral tube formation involving precipitation around a templating jet of fluid - a mechanism well-known in the physical sciences from the tubular growth of so-called chemical gardens - functions with carbonates, and we analyse the microstructures and compositions of the precipitates. We propose that there should exist biological examples of fluid-flow-templated tubes formed from carbonates. We present observational and theoretical modelling evidence that the complex structure of biomineral calcium carbonate tubules that forms the 'rose' of the watering-pot shells, Clavagelloidea, may be an instance of this mechanism in biomineralization. We suggest that this is an example of self-organization and self-assembly processes in biomineralization, and that such a mechanism is of interest for the production of tubes as a synthetic biomaterial.

STATEMENT OF SIGNIFICANCE

The work discussed in the manuscript concerns the self-assembly of calcium carbonate micro-tubes and nano-tubes under conditions of fluid flow together with chemical reaction. We present the results of laboratory experiments on tube self-assembly together with theoretical calculations. We show how nature may already be making use of this process in molluscan biomineralization of the so-called watering-pot shells, and we propose that we may be able to take advantage of the formation mechanism to produce synthetic biocompatible micro- and nano-tubes.

DNA as information: at the crossroads between biology, mathematics, physics and chemistry

On the one hand, biology, chemistry and also physics tell us how the process of translating the genetic information into life could possibly work, but we are still very far from a complete understanding of this process. On the other hand, mathematics and statistics give us methods to describe such natural systems-or parts of them-within a theoretical framework. Also, they provide us with hints and predictions that can be tested at the experimental level. Furthermore, there are peculiar aspects of the management of genetic information that are intimately related to information theory and communication theory. This theme issue is aimed at fostering the discussion on the problem of genetic coding and information through the presentation of different innovative points of view. The aim of the editors is to stimulate discussions and scientific exchange that will lead to new research on why and how life can exist from the point of view of the coding and decoding of genetic information. The present introduction represents the point of view of the editors on the main aspects that could be the subject of future scientific debate.

Directed self-assembly, genomic assembly complexity and the formation of biological structure, or, what are the genes for nacre?

Biology uses dynamical mechanisms of self-organization and self-assembly of materials, but it also choreographs and directs these processes. The difference between abiotic self-assembly and a biological process is rather like the difference between setting up and running an experiment to make a material remotely compared with doing it in one's own laboratory: with a remote experiment-say on the International Space Station-everything must be set up beforehand to let the experiment run 'hands off', but in the laboratory one can intervene at any point in a 'hands-on' approach. It is clear that the latter process, of directed self-assembly, can allow much more complicated experiments and produce far more complex structures than self-assembly alone. This control over self-assembly in biology is exercised at certain key waypoints along a trajectory and the process may be quantified in terms of the genomic assembly complexity of a biomaterial.

Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach

Mixing fluid in a container at low Reynolds number— in an inertialess environment—is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the “belly phase,” peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

The cuttlefish Sepia officinalis (Sepiidae, Cephalopoda) constructs cuttlebone from a liquid-crystal precursor

Cuttlebone, the sophisticated buoyancy device of cuttlefish, is made of extensive superposed chambers that have a complex internal arrangement of calcified pillars and organic membranes. It has not been clear how this structure is assembled. We find that the membranes result from a myriad of minor membranes initially filling the whole chamber, made of nanofibres evenly oriented within each membrane and slightly rotated with respect to those of adjacent membranes, producing a helical arrangement. We propose that the organism secretes a chitin–protein complex, which self-organizes layer-by-layer as a cholesteric liquid crystal, whereas the pillars are made by viscous fingering. The liquid crystallization mechanism permits us to homologize the elements of the cuttlebone with those of other coleoids and with the nacreous septa and the shells of nautiloids. These results challenge our view of this ultra-light natural material possessing desirable mechanical, structural and biological properties, suggesting that two self-organizing physical principles suffice to understand its formation.

Genericity of confined chemical garden patterns with regard to changes in the reactants

Typical patterns emerging during the growth of chemical gardens in a confined geometry when the concentration of the reactants are changed. These patterns are robust to changes in the reactant ions.

Dynamics of osmosis in a porous medium

We derive from kinetic theory, fluid mechanics and thermodynamics the minimal continuum-level equations governing the flow of a binary, non-electrolytic mixture in an isotropic porous medium with osmotic effects. For dilute mixtures, these equations are linear and in this limit provide a theoretical basis for the widely used semi-empirical relations of Kedem & Katchalsky (Kedem & Katchalsky 1958 Biochim. Biophys. Acta 27, 229-246 (doi:10.1016/0006-3002(58)90330-5), which have hitherto been validated experimentally but not theoretically. The above linearity between the fluxes and the driving forces breaks down for concentrated or non-ideal mixtures, for which our equations go beyond the Kedem-Katchalsky formulation. We show that the heretofore empirical solute permeability coefficient reflects the momentum transfer between the solute molecules that are rejected at a pore entrance and the solvent molecules entering the pore space; it can be related to the inefficiency of a Maxwellian demi-demon.