Hindawi Complexity Volume 2018, Article ID 9376183, 21 pages https://doi.org/10.1155/2018/9376183

Research Article Prebiotic Geochemical Automata at the Intersection of Radiolytic Chemistry, Physical Complexity, and Systems Biology

Zachary R. Adam ,1,2 Albert C. Fahrenbach ,3 Betul Kacar ,2,3,4 and Masashi Aono 5

1 Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA 2Blue Marble Space Institute of Science, Seattle, WA, USA 3Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo, Japan 4Department of Molecular and Cellular Biology and Department of Astronomy, University of Arizona, Tucson, AZ, USA 5Faculty of Environment and Information Studies, Keio University, Kanagawa, Japan

Correspondence should be addressed to Zachary R. Adam; [email protected]

Received 27 October 2017; Accepted 20 February 2018; Published 26 June 2018

Academic Editor: Roberto Natella

Copyright © 2018 Zachary R. Adam et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Te tractable history of life records a successive emergence of organisms composed of hierarchically organized cells and greater degrees of individuation. Te lowermost object level of this hierarchy is the cell, but it is unclear whether the organizational attributes of living systems extended backward through prebiotic stages of chemical evolution. If the systems biology attributes of the cell were indeed templated upon prebiotic synthetic relationships between subcellular objects, it is not obvious how to categorize object levels below the cell in ways that capture any hierarchies which may have preceded living systems. In this paper, we map out stratifed relationships between physical components that drive the production of key prebiotic molecules starting from radiolysis of a small number of abundant molecular species. Connectivity across multiple levels imparts the potential to create and maintain far-from- equilibrium chemical conditions and to manifest nonlinear system behaviors best approximated using automata formalisms. Te architectural attribute of “information hiding” of energy exchange processes at each object level is shared with stable, multitiered automata such as digital computers. Tese attributes may indicate a profound connection between the system complexity aforded by energy dissipation by subatomic level objects and the emergence of complex automata that could have preceded biological systems.

1. Introduction ways: should it consist of a subdivision into the four major polymer types that make up the cell (nucleic acids, proteins, Te tractable history of life exhibits a consistent trend in lipids, and carbohydrates) each with its own precursors and structural hierarchy, as recorded by the successive emergence settings [4, 5], an assortment of autocatalytic [6] or mutually of organisms with greater numbers of levels of nestedness catalytic [7] sets, an inferred chronological ordering of the and greater degrees of individuation at its highest levels [1– appearance of life’s universal chemical constituents [8, 9], 3]. Te lowermost object level of this hierarchy is the cell, or some other logical arrangement altogether? Additionally, but it is not clear whether this trend extended to object how far down in the hierarchy of matter do object level levels below the cell itself prior to the emergence of the Last classifcations ought to extend? Is it sufcient to stop at the Universal Common Ancestor (LUCA). As one of few trends level of small molecules? found across diverse clades of living systems, it is reasonable A synthesis of physics, chemistry, systems biology, and to infer that some corollaries of this generalized behavior automata theory may provide a constructive means of dis- were also central to the chemical processes leading to life’s tilling groups of objects that enable a living cell to emerge. origins. One critical impediment to investigating life’s origins An automaton is a machine that performs a function or along these lines is that the delineation of object levels below set of functions according to a predetermined set of coded the cellular level can be done in any number of possible instructions, especially one capable of a range of programmed 2 Complexity responses to diferent circumstances [10]. Tis broad defni- respect to how the fundamental characteristics of automata tion encompasses many diferent physical forms (instantia- (incontrasttothosecharacteristicsthatmaybereducedto tions) of objects that exhibit automaton behavior [11–13]. For wholly physicochemical mechanisms) were accumulated and example, one may describe an enzyme as a kind of automaton exhibited by prebiotic systems. Indeed, the feld of biological that carries out a catalytic function that responds to input computation is built upon the notion that life forms are instructions (i.e., a substrate molecule) to produce a specifc not just objects that may be approximated by automata; molecular output [14–16]. Some enzymes carry out catalytic depending upon how they are cultivated and observed, living functions only under the circumstance that an appropri- systems may be described as forms of automata [21, 38–40], ate energy activation molecule is available (i.e., nucleoside which are themselves composed of smaller-scale automata triphosphates such as ATP or GTP, NADP, and ferredoxins); with emergent properties that arise between and among lower others do not [17]. At a broader scale, biosynthetic pathways object levels [20, 41]. or even the entire metabolic network of a cell may be viewed At multiple organizational levels (enzymatic, metabolic as exhibiting automaton-like properties in coordinating the network, transcription/translation, and entire cellular sys- uptake of nutrients and the excretion of wastes [18]. In tems), biochemical reactions and organismal responses are these ways and many others, living organisms carry out ultimately structured by architectural information that is complex physical and chemical processes that resemble the stored in an organism’s genome. It is particularly tempting workings of automata assemblies across many diferent scales to draw an analogy between the intracellular processing of of structure [19–21]. nucleic acids and the processing of information stored in In this paper, we extend the idea of subsumed com- memory elements of the most complex class of automaton plexity [22] to map out stratifed hierarchical relationships known as a Turing machine: both systems process informa- between physical and chemical objects that produce key tion stored in a string of symbols built upon a fxed alphabet, prebiotic molecules. Tese relationships extend from sub- and both operate by moving step-by-step along those strings, atomic objects up to cells, where they join contiguously with modifying or adding symbols according to a given set of rules biological nested hierarchies. Te stratifcation of these object [41]. levels refects the division of input energy among greater Despite key diferences between biological systems and numbers of particles within the system, corresponding to devices such as Turing machines, the machine-like function- an increase in entropy. Multilevel transfer processes across ality of life’s structural components invites the possibility that diferent object levels impart emergent dynamical properties prebioticchemicalsynthesiswasmadepossiblebyautomaton best described with automata formalisms. Te circumstances behavior that emerged at the interface between chemistry and by which physicochemical automata can emerge and direct physics. Te functional requirements imposed by generalized the production of higher level objects may serve as a useful automaton system classes may thus serve as a starting point guide for reconstructing life’s origins. for assessing whether automata predecessors would have been possible under prebiotic circumstances. 2. Many Roads Lead to Rome: Continua Te specifc instantiation of a complex automaton that Connecting Abiotic to Biotic States can read, write, and store information is unconstrained; it may consist of molecules, transistors, vacuum tubes, springs, Reconstructive eforts in the origins of life have historically or even colliding objects [42–44]. Similarly, the substance and been assessed along diferent continua as new analytical confguration of a memory element may consist of switches, tools, fundamental concepts, and disciplinary advances have valves, beads in boxes, genetic sequences, or etched silicon; been developed. Each assessment is broadly similar in theory the only requirement is that the memory element be an and approach, consisting of an attempt to match the char- arrangement of stable or periodic states [42, 45]. Analogous acteristics of extant life to the characteristics of nonliving to lines of inquiry conducted in the physical and chemical settings or circumstances that may be most conducive to disciplines, one may inquire about intermediate states of life’s emergence. In the modern era, this assessment has matter capable of behaving like automata with diferent broadly unfolded along environmental [23–26], physical [27– capacities, specifcally: 29], and chemical [25, 30–33] axes that attempt to connect nonliving (abiotic) to living (biotic) states of matter in a (i) Prior to the development of informational polymers, contiguous fashion. With greater elucidation of universal did prebiotic chemical systems exhibit behaviors chemical and physical processes, comparison of possible or network patterns that may be approximated by prebiotic environments has been recast as comparison of automata formalisms? physical and chemical processes that are colocated with one (ii) What conditions or confgurations of the environ- another in any particular environment. ment may promote the development of memory Origins research has recently expanded to include com- elements, and what form(s) could such elements putational simulations of automata with emergent properties assume? that mimic or recapitulate living behaviors [34–36]. Abstract in silico automata have uncovered dynamical relationships (iii) At what stage of prebiotic chemical evolution did that, for example, can give rise to the emergence of functional substances of any object level acquire attributes func- biopolymers [37]. Beyond the scope of in silico model devel- tionally equivalent to complex automata capable of opment, though, more fundamental questions remain with chemical computation? Complexity 3

Table 1: Hierarchically compounded components and instruction levels recognizable in most modern computers, with object levels and characteristic time scales of operation in seconds. Adapted from Brown et al. [47] and Denning [48].

Level Name Objects (characteristic time scale) 5 15 Workfow process Cross-platform instructions and applications (10 ) 3 14 User interface Machine operating systems (10 ) 1 13 User virtual machine User machine displays (10 ) −1 12 Directories Directories (10 ) −2 11 I/O streams Input/output data (10 ) −2 10 Devices External devices (10 ) −2 9 File system Files (10 ) −2 8 Interprocess communication Pipes (10 ) −2 7 Virtual memory Memory segments (10 ) −3 6 Local secondary storage Blocks of data (10 ) −4 5 Processes and semaphores Primitive processes, semaphores, ready list (10 ) −5 4 Interrupts Fault handling programs (10 ) −6 3 Procedures Procedure segments, call stack, display (10 ) −8 2 Instruction set Evaluation stack, scalar data, array data (10 ) −8 1 Random access memory (RAM) Short-term memory elements (10 ) −12 0 Electronic circuits Registers, gates, buses, and so forth (10 )

Te design of modern digital computers may prove instruc- throughout a cell’s lifespan. Multiple copies of the most active tive in further breaking down these questions. Computers polymers are constructed in a cell to ensure frequency of con- and living systems are not analogous in function, but the tact and robustness of the cellular metabolic network [50]. A common attributes of their constituent automata can reveal fowofenergythroughthecellisenforcedbyspecializedand underlying trends that should apply equally to both biological complementary docking surfaces on these polymer types that and digital systems [45]. Digital computers are built upon ensure that contact between polymers is highly coordinated primitive functions involving the reading, manipulation, and specifc (Figure 1). Living organisms do not compute storage, and output of binary digits (1s and 0s) [46]. High binary digits but rather bind to and process specifc nutrients, level functions such as conducting complex mathematical excrete waste, and exhibit complex behavior individually and operations, running programs, or typing text documents are among cellular groups in relation to analog chemical signals, carried out by abstracting groups of these primitive functions digital readings of genetic polymers, internal feedback loops into more and more sophisticated algorithms within a hier- of interacting compounds, and stimuli from the surrounding archy of nested object levels. Te hierarchical compounding environment [51]. Making sense of the cell as an ensemble of instruction sets in modern computers includes at least 16 of automata requires a comprehensive, system-level approach levelsofoperation(Table1)[47,48].Tecumulativeefectsof to characterize the interactions and control networks that so many levels of abstraction are so sophisticated that most regulate and drive cellular behavior. computer programming can be done in natural languages Living systems are built upon physical and chemical or actions comparable to common human communication, interactions arranged in such a way so as to exhibit many to the extent that most users complete tasks in ignorance of (if not all) of the functional components associated with the underlying programming languages or specifc designs of the most complex classes of automata: memory elements computing devices. (genetic sequences, enzyme sequences, or at a systems level Living systems, on the other hand, function and behave in the entire cell itself), reading devices (the ribozyme reads ways that are quite distinct from digital computers. Te basic RNA; enzymes “read” substrates and nutrients in the cell), unit of life, the cell, is itself a highly complex organic machine and distinct states (activation and deactivation of enzymes capable of high-fdelity replication powered by uptake of or metabolic intermediates, or the location of the cell itself nutrients from its environment [49]. Te components of the as a state of local nutrient availability or environmental cell, namely, informational polymers such as DNA and RNA habitability). Tis distilled perspective maps the real-world and metabolic polymers such as enzymes, are part of an domain into a mechanical domain of automata formalisms elaborate network of mutually recognizable polymers that are [52] which may be used to synthesize a new reconstructive concentrated and contained within the cell membrane [41]. approach to studying life’s origins: was prebiotic chemical Tese polymeric components, and their energetic substrates, complexifcation also a process of automata complexifca- move via difusion throughout the cell volume, bringing tion? them into physical contact with one another with sufcient As a specifc example, consider the requirement that the frequency that cell upkeep and growth can be maintained most complex classes of automata that resemble the cell 4 Complexity

Network Cellular elements facilitate difusion-limited interactions between Interaction view Interaction view polymeric compounds narrows the range of settings that can Individual reactive polymers bereasonablyexpectedtoconnectLUCAwithnonliving systems. Complex behaviors of automata are ofen manifested across diferent object levels or scales of observation. Recon- structingthepotentialforprebioticautomatafrstrequires enumerationofspecifcsubcellularobjectlevelsthatspan Polymer interaction sites energy inputs and outputs.

3. Subsumed Complexity and Subcellular Object Level Recognition

Complementary docking sites specifcity, network structure Life is a far-from-equilibrium confguration of diferent Multiple copies redundancy, frequency of interaction classes of molecules. Its complexity and continuity are a Difusion speed probability and frequency of interaction result of polymeric components coming into frequent contact Figure 1: Simplifed network interaction view (a) and cellular with one another via difusion within an enclosed cellular interaction view (b) of metabolic polymers in the cellular environ- environment. Te origins of life may be considered as a ment. Metabolic network structure is maintained by complementary specifc problem involving a much broader question: what is interaction docking sites that help to narrow down interactions the origin of complexity [55] and does complexity represent among polymers to specifc functions. a quantity that can be physically measured, compared, or estimated? Subsumed complexity is the idea that the frst living cell, as a complex arrangement of atoms and molecules, was require the use of memory elements. Tere is no require- preceded by and derived from an arrangement of matter ment that memory elements take any particular physical or and energy that was at least as complex as the cell itself. By chemical form. At the subcellular level, memory elements extension, the process by which life emerged cannot be char- correspond to encoded genes. At levels immediately above acterized as a gradual increase in complexity; rather, there the cell, it is the cell itself and its system-level status as was a preexisting background of physical complexity, within persisting, reproducing, dying, dead, or translocating in whichchemicalcomplexitybecamegraduallysubsumeduntil relation to other cells around it that may be considered life emerged [22]. It is built upon the concepts of “complexity as a functional memory element. Te capacity for memory as thermodynamic depth” [56] and the relative entropy of elements to retain specifc information about past, present, diferent forms of input and output energy [57]. and future states of a system is required to manifest stable Termodynamic depth is defned as the diference local structures. � � An assessment of memory elements may be extended between the macroscale ( ) and microscale ( 0)entropyfor to conditions that immediately preceded the emergence of asystem: the cell. It is highly improbable that the very frst abiotically produced nucleic acid and peptide sequences were capable �=�−�0. (1) of catalyzing molecular reactions, if only because of the low probability that any randomly generated peptide sequence In this analysis, the complexity of a system corresponds to has such properties [53]. It is less likely that the frst generated the amount of entropy that has to be produced to generate sequences were capable of recognizing and coordinating with that object. Tis defnition is versatile (it may be applied one another in difusion-limited polymer-polymer interac- to many diferent physical and chemical systems, at many tion networks that form the basis for extant cell functionality diferent scales of observation) and instructive (it is an and individuation [54]. Tis imposes a functional require- additive property, showing that copy processes at any scale ment that pregenetic memory elements, in some form, must have almost no thermodynamic depth beyond the depth have preserved asynchronously produced polymer sequences of the original process that formed the frst copy). One of in close proximity to one another. Sequences must have its main limitations is that its classifcation of “macroscale” been preserved over sufcient time that interaction networks and “microscale” measurements is arbitrary, and it is not could arise from within a subset of many combinations of predictive of how complexity will be manifested in a system abiotically produced polymer populations. Te sequences with great thermodynamic depth. In other words, all of located within a memory element refect information about the descriptive information of a system is reduced to the the spatial and temporal patterns of physicochemical states diference between two numbers across some subjective and environmental conditions within that region of the larger threshold of measurement. One may infer that a system is system. Tis information did not have a biological context likely to be more complex than another using the analysis, until polymer-polymer interaction networks based on mutual but the underlying mechanisms that make a system more polymer recognition produced an individuated, higher object complex than another must be enumerated and described level entity. A general requirement that pregenetic memory separately. Complexity 5

Maximize: Mass）． Maximize: Chemical specifcity M1,）． M2,）． M3,）． Mass）． Direction of reactions Object levels Polymer productivity Entropy production per N－！３３ Retention of N－！３３

Mass）．）４）！， = Mass＆）．！， E1,）． N３％１５％．＃％３ Object level j Energy／５４ E2,）． Energy）． N3 (sugars, nucleobases) Energy／５４ Object level 3 E3,）． N2 (HCN, ＃（2O, etc.) Object level 2 N 1 (solvent) Energy）． Object level 1

Mass／５４ Mass／５４ (a) (b) Figure 2: (a) Mass-energy scheme of typical prebiotic experiment architecture. (b) Mass-energy scheme of subsumed complexity experiment architecture.

Te thermodynamic depth of an energy source can be in operation across these object levels. Tis should maximize approximated using a calculation of the entropy production the sophistication of energy dissipation pathways while pro- of that energy within a closed system. An approximate viding suitable conditions for automaton behavior to arise calculation for the entropy production in a system with across diferent object level thresholds. Another objective conserved mass [57] provides a means of estimating the is to eliminate the infux and outfux of mass, maximizing diferenceinmicroscaleenergyinputandmacroscaleenergy entropy production per number of massive particles in a output (i.e., contact with a thermal sink): system [56, 58]. Tis also increases the probability that larger, � =� longer-lived molecular structures can form and increase in IN OUT concentration over time in the system without being either � 2���� 3/2 dilutedbyinfuxorwashedoutofthesystem. �=�� [ ( ) �5/2] ln 2 Powerful subatomic radiation such as gamma rays max- � ℎ imizes power input normalized per number of input par- (2) �≅�� ticles. Te most notable efect of using this energy source is that powerful photons enable the perturbation of more �OUT �OUT fnelyresolvedstructuresthatmakeupmoleculesandatoms ≅ . (Figure 3). Te rules that a system follows in relaxing back to �IN �IN a ground state difer depending on the scales at which those By maximizing the ratio of the number of output quanta structures are being perturbed. producedpernumberofinputquanta,themicroscaleentropy By perturbing more fnely resolved structures, the use (�0) of a system may be minimized, thus maximizing the of more powerful input particles increases the number thermodynamic depth of a closed system in contact with of descriptive states that are required to approximate the a thermal sink at a fxed temperature. Tis approximation full range of energetic responses of molecules and atoms. provides a physical basis for inferring that systems driven by Under moderate physical conditions, coarse macroscopic fewbuthighlyenergeticinputparticlessuchasgammarays descriptions of molecules and atoms are sufcient to describe are inherently more complex than systems driven by other most induced perturbations of the system. At even more forms of energy such as infrared or visible light, even if the extreme conditions, the outermost valence electrons begin to total amount of energy inputted into and out of the system is dissociate and rearrange, emitting light commensurate with equivalent using both forms of energy. photoelectron spectra in the visible to UV portions of the It follows that, instead of searching for life’s origins among spectrum (or, conversely, when species combust, these are chemical systems that produce key prebiotic molecules of the portions of the spectrum at which light is emitted). Te interest (Figure 2(a)), one may instead search for general- perturbation of inner atomic electrons requires even more ized physical conditions in which complexity is inherently energy, typically in the X-ray portion of the spectrum. Te high (Figure 2(b)). One may then investigate whether the diferent spectra of X-ray emission are intimately associated molecules used in cellular polymers can be plausibly pro- with identifying specifc atoms through X-ray difraction. duced within these systems when they are endowed with an Probing the scale of nuclei would require highly energetic initial composition of common materials. Te objective is to subatomic particles such as gamma rays, neutrons, or highly seek out systems that maximize the number of object levels accelerated electrons or other atoms that can collide with and and therefore maximize the number of energy exchange rules transform particles at very short distances proximal to the 6 Complexity

Approximate density Graphic Formalism of descriptive states representations (attributes; photon energy thresholds)

Macroscopic thermodynamics (pressure, temperature; microwave-infrared)

Atomic and molecular transitions (rotation, vibration, vibronic emissions; infrared-visible)

Intra-atomic (valence) electron interactions (electron state transitions; visible-UV)

Inter- and intra-atomic electron orbital confgurations and structures (electron scattering and emission; UV-X rays)

Atomic structure confgurations (charged/neutral particle scattering, nuclear state relaxation; gamma rays)

Figure 3: A depiction of diferent kinds of descriptive levels of carbon dioxide molecule behavior, arranged by energy thresholds. Te use of more powerful, lower object level energy inputs is associated with the disruption of objects at fner scales of resolution that make up molecules, atoms, and subatomic particles. Te perturbation of fner scale structures necessitates accounting for higher numbers of states representing higher object densities, along with formalisms for functions and relationships particular to each level.

nucleus that fall under the infuence of the strong nuclear Te structure of this hierarchy and the relationship of force. these object levels to one another share some attributes Te overall picture is that energy in any natural system with the hierarchy of digital computers. Computers are dissipates according to a natural hierarchy, one in which constructed to translate basal physical processes into such powerful forms of energy are attenuated by fne atomic and a high level of abstraction that we are barely aware that we molecular objects as they are converted to greater num- are manipulating the precise placement of small numbers bers of less powerful particles. Simultaneously, these greater of electrons, or that the circuits themselves are composed numbers of less powerful particles are unable to perturb of ever-smaller numbers of semiconducting atoms. Tis lower level reactions, stratifying the hierarchy and efectively level of abstraction is made possible by the high number hiding the processes of energy exchange followed at these of intervening object levels which process and repackage lowerlevelsasthesystemequilibrateswithathermalsink. signals over the entire architecture of the system [42]. Atomic Teresultisthatasystemwithagivennumberofmassive scale processes are critical to achieving sufcient signal-to- particles, driven by a given quantity of energy, exhibits a noise performance so that the mechanisms function reliably broader and more complex range of behaviors if energy during every process cycle [49]. Tis degree of control is input is constrained to follow “rules” of energy fow through madepossiblebecauseatomsandgroupsofatomsstatistically lower level objects. Te rules of energy fow are efectively set function the same way and, according to very specifc by the hierarchical arrangement of subatomic, atomic, and and highly stratifed rules, across the lowermost levels of molecular components within the system. interaction. Complexity 7

Table 2: Te proposed hierarchy of nested objects relevant to comprehensive consideration of prebiotic evolution experiments.

Level Name Objects Properties 11 Consortia Groups of cells Cellular ecology Darwinian evolution: vertical inheritance 10 Cellular life Individual cells (reproduction), genetic and physiological variation, encapsulated autonomy Persistent, tractable identities based on 9 Hereditary compartments Groups of polymers difusion-governed interactive behaviors Polymer catalysis and molecule-specifc 8 Polymer interaction networks Polymers and molecules network feedback Individual polymers (peptides, Condensation reactions, nonspecifc molecule 7 Small polymers nucleotides, and phosphates) coordination Heat capacity, difusivity, convection, phase 6 Molecular thermodynamics Groups of molecules transitions 5 Molecular interaction networks Groups of reactive molecules Molecular interconversion, network feedback Interatomic vibration and rotation, isomorphic 4 Molecular dynamics Individual molecules states Valence electron movement, sharing, and 3 Intramolecular bonds Atoms and molecules displacement Electron orbital structures, X-ray, and 2 Atomic Individual atoms Cerenkov excitation and emission Protons, neutrons, electrons, and so Nuclear stability, fssion/fusion, atomic 1 Subatomic forth interconversion, gamma ray emission

Viewing a generalized prebiotic system through a physical object level thresholds. By utilizing the rules imposed on lens also demonstrates that these object levels, and by associa- energy transfer by lower object level interactions, one can tion the rules that govern interaction at any given object level, obtain greatly increased capacity to output unlikely, far-from- are themselves stratifed in a very specifc order: energy fow equilibrium confgurations of molecules at higher object in natural physicochemical systems tends to proceed from levels. Te question becomes, do any of these far-from- the bottom levels to the top levels through the process of equilibrium confgurations resemble those that seem to be energy dissipation until the temperature of the thermal sink required for the production of key biological molecules? is reached. Interactions at lower object levels involve energy Discerning object levels associated with diferent energy exchanges and transformations on much shorter physical inputs and outputs enables one to estimate where and how and temporal scales. As a unit of input energy is attenuated transformation rules at a given level should be capable of and fltered higher into the hierarchy, the energy initially efecting energy distribution at higher levels. One possible carried by few particles becomes distributed and exchanged arrangementofobjectlevelsrelevanttoreconstructinglife’s between larger numbers of particles. Entropy is manifested as origins is outlined in Table 2. Te lowermost object levels a decreasing likelihood that any single unit of input energy are set by the structural hierarchy of subatomic, atomic, and caneverbefoundinanysinglestatespaceorparticle,as molecular particles and are therefore more rigidly defned. a chain of events is set into motion that afect ever-greater Te middle and uppermost object levels are less rigidly numbers of particles in the system. defned; the molecular composition of a system driven by Another important aspect of using subatomic energy perturbation of lowermost objects changes over time, with to drive system behavior is that the resulting spatial and the result that objects at these levels may not be present or temporal distribution of the attenuated and scattered energy exert diferent efects on the overall system at diferent points particles (i.e., Bremsstrahlung X-rays, secondary electrons, of time as the system develops. UV photoelectrons, Cerenkov UV photons, etc.) carry infor- Itwouldbeamistaketodirectlyequatethephysicaland mationaboutthecompositionandstateofthetargetatoms chemical hierarchical levels outlined in Table 2 with the levels and molecules. Tis information is typically considered from of abstraction that make up the operating systems of digital a laboratory or analytical perspective with little bearing on computers; there is no direct correspondence between these driving the chemical evolution of a natural system. However, diferent systems. Nevertheless, the architectural attributes the physical forms of these pieces of information also increase of the relationships of these object levels to one another the number of rules that describe how the system can be and the diferent formalisms that succinctly relate groups reconfgured as energy moves through higher object levels. of objects within each level have properties that resemble Tis represents a vast and underexplored source of physic- abstracted computer hierarchy formalisms. Hierarchically ochemical sophistication that can drive chemical evolution nested systems start from a small set of elementary compo- of abiotic systems as energy is attenuated across diferent nents from which, layer by layer, more complex entities may 8 Complexity be constructed [52]. Shared attributes between these diferent 4. Lower Object Level Threshold Effects on hierarchically arranged systems include the following: High Level Chemistry

(i) An operating system is composed of a hierarchically Te metabolic basis of all life is the structural attenuation and organized control program for selecting and allocat- channelization of ambient energy (chemical or photonic) into ing resources among diferent tasks within a com- the coordinated production of biomass. Tis coordination puting system. Chemical compounds are selectable has become highly specialized over billions of years of components with a hierarchically organized means evolution. Prior to the development of encoded genes and of allocating the fow, attenuation, and retention of decryption protocols that compose the Central Dogma, it energy among diferent objects in a system. is unclear whether or how this level of sophistication and specifcity would be expressed in a prebiotic physicochemical (ii) Te lowermost object levels of both systems generate system. an array of statistically predictable responses of atoms Origins of life research as a chemical discipline has been and molecules to energy inputs. carried out as a search for chemical reaction pathways and conditions that preceded highly specialized biological synthe- (iii) Each level builds on the levels below but also hides all sis pathways. Experiments typically consist of diferent reac- of the internal details of its operations from the levels tive species that correspond to hierarchical level 3, conducted above. within a solvent medium such as liquid water [59, 60]. Tis (iv) A function describing activity at a given level has general experiment architecture is part of a broad-ranging, access only to functions defned at lower levels. systemic search for the production of key components of biol- ogy such as amino acids [61–63], nucleic acids [5, 33, 64, 65], (v) Stratifcation ensures that higher level objects can cell membrane phospholipids [66, 67], and reactive metabolic only emerge sequentially from functions carried out intermediates that make up the carboxylic acid cycle [68, 69] at lower levels. Tis imparts stability on the entire or the gluconeogenesis pathway [70]. Tese studies have been system. instrumental in uncovering reactions that produce biological molecules using reactants and conditions that would have A distillation of hierarchically nested interactive objects been available on the early Earth or early solar system with found within any prebiotic physicochemical system would the shortest possible list of process specifcations. However, seem to be a critical prerequisite to reconstructing life’s there have been no reports of a prebiotic chemical system that origins as difusion-constrained instantiations of automata. possesses the key hierarchical attributes exhibited by life at Without understanding the formalized groups of objects the level of the cell and higher. distinguishable by physical and chemical thresholds, the Drivingenergyintoasystematlowerobjectlevelthresh- way that entropy production stratifes the thresholds into a olds has the potential to impart novel chemical synthesis hierarchy, or the full scope of intralevel interactivity where functionality that relaxes the need to impose external manip- emergent behavior begins to manifest, it is impossible to rec- ulations to produce molecules of interest. Te most general ognize the conditions under which automaton-like behavior output of irradiating a homogeneous liquid mixture is the can originate. rearrangement of atoms and molecules to produce a mix of Tere are no a priori reasons to infer that life’s origins oxidizing and reducing compounds across a wide range of must originate or be driven from energy input at any par- redox states (Figure 4(a)). As a specifc example, consider ticular hierarchical level. However, simple rules formalized the irradiation of a simple solvent molecule like water (see at any single level can give rise to emergent complexity at Figure 4). higher levels separated by structural, spatial, or temporal A water molecule can respond in a number of diferent ways (Figure 4(b)), but most of these responses involve thresholds.Onthisbasis,itisreasonabletoinferthat ∗ entering an excited state (H2O ) or the ejection of an electron the selection of systems with the highest possible number − ∙+ of object levels between energy input and output should (e ), leaving behind a water radical (H2O )[71].Tis −16 maximize the possible complexity of the system. Te reason process occurs very rapidly, on the order of 10 seconds, is quite simple: each additional hierarchical level opens a much shorter than the duration of typical molecule-molecule capacity for sophistication through the imposition of new collision frequencies. Tese frst-generation products interact system rules at that level and another potential degree of with one another or, more likely, with other surrounding nestedness that can be organized using objects drawn from water molecules to produce a second generation of products ∙ ∙ − the level immediately below. As each level imposes its own such as H or OH radicals or a solvated electron (eaq ), unique set of exchange rules on the overall system, greater which is an electron that is thermalized and surrounded by sophistication should be aforded between system input and a loose cage of water molecules. Tese second-generation system output. Greater sophistication afords fewer external products interact with one another and other water molecules constraints that need be applied to reach a desired output on longer time scales to produce an array of third-generation state. By extension, the only external constraints that need to products such as hydrogen peroxide, hydrogen or oxygen be applied should be the initial composition of atomic and gases, OH and H ions, or more solvated electrons. From the molecular components, the energy input, and the thermal initial state to the fnal state, the processes are essentially sink temperature. unidirectional and occur within a very small radius. All of Complexity 9

− + − ／2 O（ （2／2 （ （2 ？；Ｋ −7 10 Ｍ ∙ ∙ + ∙ − （ + OH （ + OH ？；Ｋ 10−10 Ｍ ∗ ∙+ − Oxidizing Reducing （2／ （2／ ？ 10−13 Ｍ Solvent molecule （2O 10−16 Ｍ Subatomic radiation , , , N radiation

(a) (b)

Figure 4: Irradiation of water by energetic subatomic particles. Based on Lousada et al., 2016.

these reactions are so rapid and so far from equilibrium of chemical structures to create higher object levels. Te that they are essentially instantaneous step changes in the functional result is that each level builds on top of the levels statesofthoseatomsandmolecules;theyoccursorapidly below, but the internal details of operations at the base levels andtosuchalocalizednumberofatomsandmoleculesthat are efectively hidden from the top levels. the overall process is nearly isothermal. In a heterogeneous Tis simple array of lower object level reactions drives liquid mixture, the fnal products persist and difuse far away thesystemathigherlevelsinmultipleways.First,itisnot enough from the point of formation that they interact with necessary to introduce implausibly high concentrations of other molecular species; the efciency of this process depends reactive compounds to drive the system; the solvent itself − in part on the energy transfer characteristics of the type is driven to produce highly reducing (e.g., H2,eaq )and ∙ of irradiation. In total, this multistep process traverses the oxidizing (e.g., O2,H2O2,and OH) species, which creates subatomic, atomic, and intramolecular bond levels and the high chemical potential throughout the solvent. Second, the products can then interact with other molecules to form new solvated electron and hydroxyl radical are efective drivers covalent bonds. of reducing and oxidizing reactions, respectively, among − ∙ Energy exchanges that occur at these lowermost levels organic species in a system. Te eaq and OH can act are fundamentally diferent than those of higher levels. sequentially and quickly on organic compounds composed of Subatomic and atomic perturbations are approximately uni- many diferent atomic species and masses, without requiring directional processes and are not specifc to any particular the introduction of new material to the system [72, 73]. atomic or molecular species. Unidirectionality arises because Tismeansthatasystemthatisclosedintermsofmass energy attenuation occurs on time scales that are much fow, but open in terms of energy fow (powerful subatomic −16 shorter (10 s) than intermolecular bombardment times particles in, thermal sink photons out), can be driven far from −10 − (10 s) and the attenuation objects (subatomic particles such equilibrium within a short period of time. Te action of eaq ∙ as electrons) are much shorter than the characteristic sizes and OH is both constructive and destructive of objects found of molecules. Overall charge balance in the system remains at higher object levels. All of these factors taken together essentially constant. Tis has the efect that fragmentation mean that entropy production per molecule can be very high of molecules into a higher number of excited or reactive over both short and long time scales without leading the objects generated in a single high energy event is eventually system to a chemically unreactive dead end. reducedbacktoapproximatelythesamenumberofstart- A critical question from the perspective of life’s origins ing molecules. Tis lack of specifcity regarding reactions remains:candrivingasysteminthismannerhelptoalign between atomic or molecular fragments, an efect at least abiotic and biotic chemical synthesis pathways? Compounds partly attributed to the nature of the highly reactive radi- derived from the radiolysis of water, combined with the cal intermediates formed, causes these exchange processes interactions aforded by the solvated electron and hydroxyl to resemble primitive, generalized functions or operations radicals, drive an array of irreversible reactions involving rather than equilibrium chemical reactions. Continued irra- simple organic and inorganic compounds that produce key diation generates a frst generation of products, and as these biological molecules. Te following paragraphs are intended products accumulate in concentration, the same generalized togiveafewexamplesofsomeofthereactionsthatcantake functions that created the frst generation begin to transform place under geologic settings that combine a source of power- a small number of these initial products into a new array of ful radiation (uraninite or other radioactive minerals); com- second-generation products. Selectivity of product formation mon molecular species found at the Earth’s surface such as can begin to arise at higher object levels through diferent water, dissolved salt, carbon dioxide, and nitrogen gas; apatite rates of reaction between diferent reactive intermediates as a potential source of phosphorus for nucleotide sequences andcompoundsthatbegintoaccumulateovertime.Such and energy transduction molecules, and pyrite as a source primitive operations are therefore likely to result in far- of iron-sulfur clusters found in electron transport chain and from-equilibrium outputs throughout all hierarchical levels other key energy transduction metalloproteins [74, 75]. ofthesystem,particularlyastheenergystoredinfar-from- Gamma rays and X-rays can cause inert gases such as N2 equilibrium species at lower levels drives reorganization and CO2 to fragment such that N and C may recombine with 10 Complexity

atoms derived from water, leading to compounds like NH3 ring will undergo another cyclization reaction with GLA and HCN [76, 77]. Bielski and Allen showed that gamma to furnish a mixture of 2-aminooxazoline stereoisomers, radiolysis of aqueous potassium cyanide (KCN) generates including the arabinofuranosyl-aminooxazoline, a key inter- formaldehyde (CH2O)throughamechanismpossiblyinvolv- mediate in the potentially prebiotic ribonucleotide synthetic ing HCN reduction by the solvated electrons produced in situ pathways demonstrated by both the Sutherland and Powner ∙ [78]. In the same mixture, OH, the hydroxyl radicals formed, groups [64, 94]. Furthermore, the Szostak group has shown attacked cyanide anions leading to formamide (FA) and that 2-aminoimidazole (2NH2Im), a potent leaving group in cyanate. Te authors also observed glycine and cyanamide the context of activation chemistry for nonenzymatic RNA (H2NCN) as products of radiolysis. It is insightful to mention replication [95], and 2NH2Ox are related products from the that the Sutherland group has demonstrated that solvated same reaction network, involving H2NCN, GA, and NH3, electrons generated photochemically by UV irradiation of in which lower pH and higher NH3 concentrations favor copper cyanide complexes in the presence of excess cyanide greater 2NH2Im production [96]. We speculate that aqueous can initiate a Kiliani-Fischer type homologation mechanism mixtures of NH3, HCN, and NaCl when exposed to ionizing for the synthesis of simple sugars, like glycolaldehyde (GA) radiation have the potential to form H2NCN, GA, and GLA and glyceraldehyde (GLA) [79], providing an alternative to and thereby higher level products such as 2NH2Ox, 2NH2Im, the formose reaction commonly invoked for prebiotic scenar- and arabinofuranosyl-aminooxazoline through a common ios [80]. Draganic´ and coworkers reported their observation reaction network taking place in a single mixture. We stress, of glycolaldehyde, ribose, and glucose arising from radiolysis however, that, to the best of our knowledge, such a reaction of aqueous acetonitrile solutions [81]. It is tantalizing to network has yet to be reported. imagine that ionizing radiation like gamma rays may be able Te resulting arrays of potential reactions are diverse, to drive a Kiliani-Fischer homologation mechanism [82]; and compounds that serve as initial reactants (H2O, CO2, however, such a radiolytic mechanism for the synthesis of N2, NaCl, pyrite, and apatite) are all plausibly found on simple sugars has yet to be explicitly demonstrated to the best an abiotic Earth and require no preparation or treatment of our knowledge. prior to irradiation. One signifcant question regarding the Te presence of iron pyrite [83] (FeS2) and apatite chemical plausibility of the entire system is whether minerals [84] ((Ca)10(PO4)6(Cl,F)2) in radioactive deposits opens a containing radioactive elements such as U or T would have pathway to release abundant phosphoric acid. FeS2 acts as a been present and concentrated within a newly formed plan- sink for oxidizing compounds such as O2,releasingabundant etary crust. Tere are difering opinions about the likelihood 2+ ferrous iron (Fe ) and sulfuric acid (H2SO4), and imparting that the early Earth crust was highly diferentiated or closer a redox and acid asymmetry to the system [85]. Sulfuric in composition to the primitive mantle [97–99]. Te only acid can then degrade apatite, releasing soluble phosphoric requirement seems to be that there were at least some areas of acid (H2PO4) and precipitating solid-phase gypsum from the the Earth’s surface, even relatively small areas, with felsic rock solution (CaSO4) [86]. Te net result of coupling between types such as granites that concentrated uranium minerals apatite and pyrite under radiolytic conditions is localized within a few hundred million years of Earth’s formation release of dissolved phosphate and degradation of pyrite, [100–102]. Tese rocks would then have been weathered which may enable the incorporation of pyrite-derived iron- andreworkedjustastheyhavebeenthroughoutmostof sulfur clusters as part of protometabolic polypeptides. Earth’s geologic history. Tis possibility opens up multilevel Alpha radiolysis of aqueous solutions of common salt physicochemical confgurations and interactions that could (NaCl) has been shown to lead to the formation of sodium have enabled emergent automaton-like behaviors. hypochlorite (NaOCl) [87]. Te reaction of hypochlorous acid (HOCl) with cyanide anion (–CN) is known to produce 5. Discussion cyanogen chloride (ClCN) very rapidly, characterized by 9 1 1 5.1. Geochemical Automata across Object Levels. Automata a second-order rate constant of 1.22 × 10 M– s– [88]. are rarely discussed in a geologic context. Most geologic ClCN reacts with imidazole to yield diimidazole imine events are reducible to physical (sedimentation rates, material (Im2CNH), an activating agent for ribonucleotides yielding transport properties, magma heating and cooling processes, the corresponding phosphorimidazolide [89], substrates of mantle convection cells, etc.) or chemical (mineral crystal which have been extensively employed in the study of formation from magma melts, ion dissolution and transport, nonenzymatic template-directed synthesis of RNA [90]. Tis mineral alteration under heat and pressure, etc.) analyti- activation chemistry has been shown to occur in one pot, cal approaches. Tere are, however, phenomena exhibiting by slowly adding NaCN and NaOCl to a solution containing � feedback or iterative network behavior best approximated by imidazole and one of the four canonical 5 -ribonucleoside automata-like descriptions. Cellular automata in particular monophosphates. ClCN when mixed with ammonia (NH3) are used to great efect for discretized macroscale systems isknowntoyieldcyanamide(H2NCN)[91],asdoesUV forwhichstateorphasechangesarehighlycontingentupon andelectronradiolysisofaqueoussolutionsofammonium localized interactions, such as subsurface fow through a cyanide (NH4CN) [92]. Te Sutherland group has shown lattice network [103], mineral recrystallization [104], solute that H2NCN and GA will undergo a cyclization reaction transport and mineral dissolution [105], or seismic wave catalyzed by inorganic phosphate acting as a general base to propagation [106]. Investigators have previously acknowl- form 2-aminooxazole (2NH2Ox) [93]. Tis fve-membered edged that automata may best approximate critical prebiotic Complexity 11 reaction networks [107, 108], but such observations were not concentrations of all of these compounds are likely to remain developed in sufcient detail to yield specifc physical or in the millimolar range or less. Cycles of heating + drying and chemical hypotheses. cooling + wetting are ofen invoked as ideal circumstances for Many mechanisms or external conditions invoked in nonenzymatic polymerization [4, 112, 113]. Te parameters of prebioticscenariosarepresumedtofunctionlikeautomata the required heating system are stringent in geological terms: even when this is not explicitly stated. Tere is little in geology a thermostat with a maximum temperature tuned just above that remains constant for long. Temperature fuctuations are the boiling temperature of water, an ambient temperature and forecastable within envelopes but are not precisely repeatable pressure that permit liquid water, a duration of heating on the or predictable. A constant-temperature setting, or even a order of tens of minutes to hours that is followed by cooling to discrete series of changing temperature phases of variable ambient conditions, an ability to periodically switch between duration, can only be a result of either complete chance for heating and cooling states, prolonged operation of a repeating a short period of time or an emergent mechanism that can heating/cooling cycle over hundreds or thousands of years, sense, and precisely respond to, stochastic external conditions and replenishment of reactive precursor molecules. over long periods of time. Bringing multiple, difering, and One means of meeting all of these stringent heating ofen conficting steps and external conditional constraints requirements is provided by water-moderated fssioning of of prebiotic chemistry into alignment remains an ongoing uranium [101, 114] (Figure 5). On the early Earth, the 235 challenge for origins research. As a result, evaluation of fssionable isotope of uranium, U,wasenrichedinexcess prebiotic plausibility typically includes at least a cursory of 20% of all planetary U (today, it is less than 1%) [102]. One 235 assessment of how broadly permissible a range of conditions of the decay paths of Uisviafssion,whichemitsnucleus may be for a studied reaction or process. If the range is decay fragments and an average of just over 2 neutrons per narrow, an assessment will describe environmental settings decay event. If U-bearing deposits on the early Earth also con- which include at least one selected variation (among many tained abundant hydrogen-bearing compounds such as water possible variations) of conditions that adequately conform to or reduced organic compounds, the neutrons are quickly a required laboratory regimen. slowed through neutron-hydrogen collisions, moderating the Enumeration of objects and object level thresholds is a neutrons and setting up conditions by which another fssion prerequisite to identify automaton-like behaviors in a physic- event can occur. Tis continues a chain reaction of events that ochemical system. Rather than seek a relatively narrow set maintains the release of abundant, highly energetic subatomic of functional conditions among many possible stochastically particles. Te resulting volumetric power density and total variable natural combinations, or a special array of initial con- amount of energy released are many orders of magnitude ditions, an alternative approach would be to seek out naturally above even the most energetic redox processes found at the occurring circumstances in which automata arise by virtue of Earth’s surface [115]. 235 intralevel emergent properties. Such automata may assist in A mineral deposit with sufcient Uandwateror driving the system through relatively restricted or improbable organic compounds functions according to a feedback system states that link abiotic and biotic confgurations of matter. Te [116]thatisbestapproximatedasaclassofautomataknownas remainder of this paper will describe two diferent kinds of a fnite state machine. Tis machine approximation has two multilevel interactions that resemble attributes or necessary states, On and Of, which meets the minimum requirement components of automata that may be worthy of further study. of a periodically operating system achievable by toggling between these states. Neutrons are moderated in the On state, 5.2. Automata 1: A Geochemical Termostat with Repetitive as each emitted neutron induces an average of at least one Operation Algorithm. Radiolysis of the selected system is more fssion event in a chain reaction. Each fssion event likely to produce intermediate compounds that can lead to releases hundreds of mega-electron volts of energy emitted oligomer formation under some circumstances, but without as a mix of �, �, �, and N and fssion recoil fragments at fux heating the dominant chemical component of the system is rates powerful enough to quickly heat the reactor core. likely to remain water. Water can result in the hydrolytic Te heating process continues until the temperature rises cleavage of the amide bonds in peptides [109] (especially abovetheboilingtemperatureofthewater(orthatofthe at extremes of pH) and RNA phosphodiester bonds [110] moderatingfuidifitiscomposedofamixoforganic (particularly in the presence of divalent metal cations) over compounds), driving the water from the fssioning uranium- relatively short timescales and is therefore not an ideal rich deposit as pressurized steam. With the loss of neutron- medium for facilitating some of the molecular network reac- moderating, H-rich fuids, the reactor enters a quiescent Of tions that may be required to reach interacting polymer object state. Te deposit cools and the moderating fuid condenses levels. Additionally, many of the reactions that link these andfowsbackintotheU-richzone,resettingthecycle. intermediate compounds to the production of nucleotides Te transition between On and Of states repeats itself until work best at high compound concentrations and, in the water is driven completely from the system and is unable 235 specifc case of nucleobase (NB) condensation from FA, to return, or the U fuel is expended, pushing the reactor desiccated and heated liquid mixtures [111]. All of these com- below criticality thresholds. In the case of well-documented pounds have a boiling temperature greater than that of water. natural fssion zones at Oklo, Gabon, subsurface fssion zones Without a means of increasing the temperature of the system operated on approximately 30-minute duration On and 150- above the boiling temperature of water (but not so high minute duration Of cycles for over 500,000 years [117]. Power that the compounds themselves are thermally degraded), production longevity and density are aforded by the high 12 Complexity

Approximate heating process algorithm: Polymer interaction >100∘ >10 ＧＣＨＭ 8 (1) Heat to C for networks (2) Cool to ambient temperature (3) Repeat (1) and (2)

（2／？ＲＮ？ＬＨ；Ｆ (t) Inorganic C 7Small polymers compounds

+ + 235 U fission N,,, ＃ＩＬＡ T）． T／５４ zone criticality radiation synthesis − Molecular 6 thermodynamics T＜ＩＣＦＣＨＡ system (（2／+＃ＩＬＡ) Molecular thermodynamics-scale temperature modulation Atomic-scale neutron moderation 91＋Ｌ Molecular interaction 36 5 Subatomic-scale energy release networks n n n （ 142 235 2O 235 56＂； 92５ IF sufcient U is present 91 （ 36＋Ｌ 2O 91 （ ／ 4 Molecular dynamics n 36＋Ｌ AND 2 is present n AND T

235 Figure 5: An approximated temperature feedback control diagram of a natural U water-moderated and cooled fssion zone. Termostatic feedback is an emergent property spread between subatomic, atomic, and molecular levels of energy attenuation. Te maximum temperature of the thermostat is governed by the boiling temperature of the moderating fuid, which is most likely water but may also include organic carbon compounds produced via radiolysis of inorganic carbon.

densityofthefssionenergysourceitself.Teoverallsystem accumulate key reactive molecules in the system to form, behavior is robust, and parameters such as peak temperature degrade, and reform many diferent combinations of polymer or duration of On-Of cycling can vary slightly depending on sequences using these molecules. An ensconced environment burial depth, permeability of the U-bearing deposit, distance wouldalsobeshieldedfromlarger-scaleperturbationsto from the fssion zone, and the degree to which the water in the Earth’s surface such as intermittent meteorite impacts, the system is connected to a larger external reservoir. Fission solar fares, or climate variations that may hinder prebiotic zones formed within short distances of one another intro- system development. Te rapid and highly localized heating duce another object level of molecular production, namely, would set up convective fows that carry the lower level convective exchange between adjacent zones of difering object radiolysis products a few meters from the fssion zone, chemical composition or maximum temperature. which is beyond the penetration depth of most forms of sub- A water-governed fssion thermostat increases the robust- atomic radiation. Convective displacement of the precursor ness of synthesis pathways between lower and higher object molecules for sugars, amino acids, and polymers increases levels of interest to life’s origins. Radiolysis is known to the likelihood that these higher level object compounds produce potential condensing agents such as cyanate and willescapeanddifusefromthefssionzoneandintothe cyanamide, but heating cycles such as this supplement these surrounding rock matrix. reactions by driving dehydration/condensation reactions by removing water from the system on scales of minutes to hours. Tis evaporation of water would also increase the 5.3. Automata 2: Hereditary Precellular Compartments—Rock concentration of the reactive intermediate compounds while Matrix Pore Spaces as Memory Elements. Te most complex driving out other compounds with boiling temperatures forms of automata are able to store information about below that of water, increasing the rates at which higher level past time states or functions across multiple time steps in molecular objects can form. Te geologic duration of such memory elements. Tere are few formal constraints on the features (>100,000 years) afords a great deal of time in an construction of such memory elements; they may be 1-, 2-, or ensconced, near-surface environment that can produce and 3-dimensional in arrangement, and they may be composed of Complexity 13 nearly any spatially or temporally organized, discrete objects automaton. Atoms and molecules fowing along these paths at any scale [45]. wouldhaveonlyaveryshortperiodoftimetointeractwith Life has optimized a universal polymer-based genetic any other groups of molecules before exiting the system. system that encodes nearly all of the information required to By defnition, 1D paths located adjacent to one another can replicate cells across generations. One of the most daunting have little conceivable interaction with one another, meaning challenges in the origin of life is simultaneously producing that the total informational content of each memory element genetic monomers and polymers, polymeric polypeptides, (however it would be defned) would be isolated from all and energy transduction molecules, with high concentrations others with limited interconnectivity. Tis limitation would andinsuchcloseproximitythattheymayallinteractwithone efectively impose the constraint that all prebiotic synthesis another at difusion-limited rates. Noncellular compartments reactions must occur in the time between the entry of objects housing mixtures of lower level objects with persistent, intotheheartofthechimneyandtheexitofthoseobjects hereditary chemical features (i.e., spanning time without at the oceanic interface. For these reasons, it is difcult to becoming well mixed with surrounding volumes) are one imagine the content or arrangement of characteristics within means of maintaining high concentrations and localized a 1D difusion-limited memory element being constructive or chemical gradients. Hydrothermal vent chambers [26, 118], cumulative over time. self-assembling lipid vesicles [119–121], rock pores [122], A 2D difusion-limited array of memory elements can pyrite mineral surfaces [32], and sediment pore spaces [116, form at any location where new, reactive material can be 123] and other structures have been described as possible introduced at diferent points of the surface. A sediment- prebiotic compartments that preceded the emergence of water interface, the mineral faces of pyrite crystals, or rocky LUCA. surfaces of exposed crustal rocks are all locations that would Automata theory, combined with physical difusion meet these requirements (Figure 7). Tese settings would parameters, may provide a means of evaluating the likelihood line a well-mixed basin that brings new molecular species that these diferent environments are capable of manifesting to the surface via basin-surface difusion and gravitational some form of complex automaton that includes memory settling of products produced in the column above the surface elements that function in this way. It is unclear at what point itself. Once brought into contact with the surface, reactive or in what form memory elements related to the genetic molecular species may difuse outward to interact with other code may have originated. However, the physics of difusion molecular species that have accumulated or been produced are general enough that one may assess the constraints by through other processes. A practical upper limit on the which distinct groups of polymer-based memory elements number of individual sources that may be found on a source mayinteractwithoneanother.Oneapproachwouldbeto of this type would be related to the physical size of a source focus on the density, dimensionality, and difusion-limited molecule and the rate at which new source molecules can be interconnectivity of compartments as memory elements. delivered to the surface, which would be correlated with the Te average difusion distance as a function of time is productivity in the overlying column. defned similarly for 1D, 2D, and 3D systems. It is approx- Te connectivity and difusion characteristics of 3D com- imately the square root of the product of q��,where� partments would seem to be best suited as memory elements. is proportional to the dimensionality of the system (2 for Compartments would have multiple axes of interaction with 1D, 4 for 2D, and 6 for 3D), � is the difusion constant the nearest neighbors, which means that a difusing com- for compounds which is proportional to each compound’s pound can reach more adjacent compartments in a shorter molecular mass and physical size, and � is the approximate period of time, increasing the density of memory elements amount of time that a compound may be allowed to difuse (Figure 8). A 3D array of elements could also be broken in the system. For all systems, � may be allowed to become into 1D or 2D memory elements under certain conditions. large to connect distant memory elements, but this comes Inhibiting free fow could reduce a set of 3D elements into at a cost of reducing the total number of memory elements adjacent 1D or 2D elements, and phase changes such as possible within a system of a given size and, more practically, evaporation could reduce 3D volumes to a network of 2D- a decrease in the efective concentration of those molecules in lined surfaces of residual compounds along pore space walls. the system. Memory element density, which is related to the As described in the section above, uranium-rich sedi- total capacity to retain information about past states within ment deposits with water in interstitial void spaces on the a defned characteristic distance, requires a clear tradeof early Earth have already demonstrated complex, emergent between system dimensionality, compound size, and time attributestypicallyassociatedwithafnitestatemachine step duration. capable of toggling between On and Of states [117]. Void 1D difusion-limited memory elements would take the spaces in such deposits may also be predisposed to serving form of discrete paths along which an object would be as a 3D difusion-limited memory array. Many uranium-rich subjected to an array of physical and chemical conditions. An rocks originally derive from minerals found in granitic rocks example would be the fow paths taken by molecules through that make up continental crust. Such rocks also include other a hydrothermal vent chimney (Figure 6) (disregarding for mineral types that are central to origins of life research such a moment the efects that fow would impart on mixing as pyrite, apatite, and rutile [111]. One particular kind of subdivided portions of the path). From a physical perspective, early Earth deposit that hosted uranium-rich rocks such as it is not clear whether memory elements of this confguration uraninite is known as a heavy mineral placer [116]. Placer would be capable of functioning efectively as part of an deposits are composed of a high proportion of minerals that 14 Complexity

Hydrothermal vent interiors (3)

(2)

(1)

Δx Length: L４／４

(1)

(4) (2)

(3)

(4) L N ≈ ４／４ 1D,－！８ 2D Deborah Kelley, 2007 (a) 1.0E + 06 D =1E−10 D =1E−9 1.0E + 05 (mem D=1E−8(membranebrane phosp pr otein) D=1E−7(poly 1.0E + 04 nucleotideholipid) D=1E− (large protein) D=1E−5 ) 6 (sm 1.0E + 03 all protein) (small molecule) 1.0E + 02

elements per meter elements 1.0E + 01 Maximum number of 1D of number Maximum 1.0E + 00 1 Ｍ？＝ 1 ＧＣＨ 1 hour 1 day 1 year Characteristic time step (b)

Figure 6: (a) Simplifed depiction of example 1D memory elements as chambers within a hydrothermal vent chimney complex. White shading across horizontal bars (lef) corresponds to regions along four diferent sample pathways through the complex (right) which are net sources of a compound of interest. (b) Maximum number of 1D difusion-limited memory elements per meter. Te width of the lines in plot (b) ∘ ∘ corresponds to variation caused by temperatures ranging from 20 Cto250C. Vent chimney image modifed from original by Deborah Kelley, 2007. are dense and resistant to weathering. Placer minerals are zircon, or pyrite. In some zones, reactions will occur that sorted by hydrodynamic forces in environments that contain are net producers of reactive biomolecular intermediates, moving water such as beaches, rivers, and creeks, ofen and in other zones reactions will predominate that are net collecting in these places where water speed is fastest. Typical consumers of such compounds. In this way, mineral hetero- early Earth placer deposits could also include silica, monazite, geneity undergirds broader molecular interaction network ilmenite, magnetite, zircon, and garnet, with grain sizes heterogeneity. typically corresponding to fne to coarse grained sandstones. Cells contain within their genomes a precise record of A heterogeneous mix of mineral grains made of placer all structural components required to make copies of them- sediments are an advantageous setting for precellular com- selves. Prior to the emergence of a cellular entity, it is unlikely partments for many reasons. Sandstones readily allow the that predecessors of all organelles, metabolic pathways, and fow of fuids and the difusion of dissolved compounds polymer types required for LUCA to reproduce on its own through interstitial pore channels. Tis ensures that zones would be found in a single void space by chance. It is more of intense radiolytic energy fux or key molecules would be likely that a great deal of time, close proximity, and difusion- well connected to one another and that the entire volume driven mixing were required before polymer sequences contributes to the memory capacity of the overall, multitiered of diferent types (i.e., polypeptides and polynucleotides energy dissipation system. Heterogeneous distributions of enclosed within lipids; object level 8, Figure 9) formed that mineral grains would mean that some pores are lined by were mutually recognizable and reinforcing of one another’s more key source molecules for reactive intermediates such formation. as phosphate found in apatite or monazite, while others Void spaces could have served critical roles as memory would have pores lined with catalytic minerals such as rutile, elements by giving some spaces or zones a consistent identity Complexity 15

Water/sediment interface Atmosphere/planet interface

Δx A４／４ N ,－！８ ≈ Area: A４／４ 2D 4D

(a) 1.0E + 12 D = 1E − 10 1.0E + 11 D=1 2 1.0E + 10 E−9 (membrane protein) 1.0E + 09 D=1E−(membrane phospholipid) D=1E−78 1.0E + 08 (polyn 1.0E + 07 D =1E−6 ucleotide) D=1E−5 (large protein) 1.0E + 06 (sm (small amolecule)ll protei 1.0E + 05 n) 1.0E + 04 1.0E + 03 1.0E + 02 elements per meter elements 1.0E + 01 Maximum number of 2D of number Maximum 1.0E + 00 1 Ｍ？＝ 1 ＧＣＨ 1 hour 1 day 1 year Characteristic time step (b)

Figure 7: (a) Simplifed dimensionless depiction of example 2D memory elements as subdivisions of lining surfaces of basins (top) in which compounds of interest are produced (bottom, shaded regions). (b) Maximum number of 2D difusion-limited memory elements per square ∘ ∘ meter. Te width of the lines in plot (b) corresponds to variation caused by temperatures ranging from 20 Cto250C.

defned by those reactions that would cause them to serve rather than minerals) is approximately 20%. Based on these as net sources or sinks, and serving as an enclosed volume fgures, there are approximately 1.7E11 distinct pore spaces in in which the products made in previous time steps could a single cubic meter of host rock, so each unique combination accumulate and interact with products of adjacent spaces would likely be sampled many times over within every cubic in future time steps. By connecting disparate voids that act meter of host sandstone. as sources and sinks for diferent portions of a molecular Referringbacktotheplotofmaximum3Dmemory interaction network, the probability of forming a higher elements in Figure 8(b), at 1E11 elements per cubic meter, object level grouping of interactive polymers is increased. freely difusing small molecules and small proteins would An estimate of the number of unique combinations reach adjacent pore spaces within about a minute, while of mineral-lined pore spaces of this approximate diversity larger compounds such as large proteins and nucleotides (�=10) and number of bounding minerals (� varies would reach adjacent pore spaces within 1 and 10 hours, from roughly 6 to 8, depending upon packing confguration) respectively. A model system with parameters matching a can be calculated. Te appropriate estimate is provided by typical surface geyser or fssion-zone thermostat (heating combinations (the order or specifc arrangement of minerals On-Of cycles approximately every hour [117]) would just surrounding the void space does not matter) with repetitions barely be within the requirement for efciently difusing RNA allowed(anynumberof6to8objectsdrawnfromeachofthe sequences to adjacent pores during each characteristic cycle categories is selectable without limit). Within these parame- step of the system. ters, there are between 5,005 and 24,310 unique combinations From a slightly larger perspective, there is an upper limit of minerals that can line a pore of this confguration. For on the lifetime difusion distance of a typical RNA sequence medium-grained sandstone, the average pore diameter is set by the rate of hydrolysis of its bonds. Te half-life of approximately 130 microns, and the void space of the overall a phosphodiester bond is about one year [110] in water at rock (the proportion of the total volume that is empty space room temperature. Te maximum difusion distance for a 16 Complexity

Mineral interstitial (pore) spaces Vesicle protocells (A) (B)

“Heredity” Assembly

environment

“Mutation”

V４／４ N3 ,－！８ ≈ D (6D)3/2 Volume: V４／４

20 Δx 15

10

5

20 15 20 10 15 10 5 5 (a) 1.0E + 18 D = 1E − 10 1.0E + 16 D= 1E−9 3 1.0E + 14 (memb D=1E−8(memb rane protei D= rane phospho 1.0E + 12 1E − 7 (polynucleotid n) D=1E−6 (large protein) lipid) 1.0E + 10 D = 1E − 5 e) (small prot 1.0E + 08 (smal ein) l mole 1.0E + 06 cule) 1.0E + 04 elements per meter elements 1.0E + 02

Maximum number of memory of number Maximum 1.0E + 00 1 Ｍ？＝ 1 ＧＣＨ 1 hour 1 day 1 year Characteristic time step (b)

Figure 8: (a) Simplifed dimensionless depiction of a sample volume subdivided by mineral grains or vesicle protocells (top) into a 3D array of adjacent memory elements with difering local concentrations of a compound of interest (shaded blocks, bottom). (b) Maximum number of 3D difusion-limited memory elements per cubic meter. Te width of the lines in plot (b) corresponds to variation caused by temperatures ∘ ∘ ranging from 20 Cto250C.

free polynucleotide in that time would only be less than 1 of a self-reinforcing network of catalytic RNA sequences centimeter. Note that these are all approximations for ideal, would help to overcome abundance and concentration limi- difusion-only scenarios. Convection could shorten molecule tations within a volume, but high abundance and productivity travel times but would also greatly dilute the molar concen- do not fundamentally overcome the difusion-limited time trations of these compounds. In real systems, surface friction and distance constraints for RNA sequences migrating out and irregular constrictions would lengthen molecular travel of a source volume and into contact with other polymer times between pore spaces. types unless the sources of compounds that compose these Tis spatial limitation indicates how severe difusion- sequences are in abundance and continuously replenished. limited transport becomes for the exchange and interaction For these reasons, it is likely that RNA sequences must among the class of compounds commonly invoked for RNA also have come into contact with zones containing other World scenarios. At an efective difusion range of less polymer types such as polypeptides that were generated than 1 centimeter per year, it is important that prebiotically in a combinatorial manner and that the combinations of generated RNA sequences come into contact with reactive these polymer productivity zones should be explored within prebiotic compounds, substrate molecules, source minerals, millimeters or centimeters of one another. In an ideal system, reactive catalysts, and other polymers on time scales much these polymer productivity zones should be directly adjacent shorter than the half-life of bond degradation. Te emergence to one another or include pore spaces where conditions are Complexity 17

Level Name 11 Consortia 10 Cellular life 9Hereditary Interstitial pore spaces as 3D memory elements compartments Approximate mineral diversity (n = 10) of a Precambrian radioactive placer: (i) Silica (ii) Monazite (iii) Pyrite (iv) Rutile (v) Ilmenite (vi) Magnetite (vii) Zircon (viii) Apatite (ix) Garnet r = 6 r = 8 (x) Uraninite Approximate number of surrounding grains: (i) r = 6 (2 for each axis) to r ≈ 8 (cubic packing) (ii) repetitions of each mineral type allowed

(r+n−1)! Unique combinations = = r! (n −1)! 5005 to 24310 Lipid condensation Polymer Oligopeptides （2０／4 8 interaction PPi GLA networks Oligonucleotides Polyphosphates CN-NH2

Figure 9: Inferred polymer production pathways at object level 8 enabled by chemical reactions from object levels 1–7 and mineral diversity combination estimates for compartments composed of placer sediment mineral grains at object level 9. suitable for the production of multiple polymer types. All of exchange processes across so many levels open the possibility these facets of time, distance, and productivity for prebiotic forsophisticatedmeansofchannelingenergyinputatlower RNA monomers indicate that source mineral heterogeneity levels into far-from-equilibrium outputs at higher object on scales of millimeters to centimeters may be an implicit levels.Teseattributeslendstabilitytotheoverallsystemand prerequisite feature of RNA World scenarios. enable the sequential emergence of higher level objects that have the potential to link abiotic and biotic states of matter. 6. Conclusions It is currently impossible to assess with certainty whether all of the inherent systemic complexity driven by subatomic- One of the implicit attributes of “complexity as thermo- scale radiation is required for life’s emergence. It is possi- dynamic depth” is that greater thermodynamic depth can ble that chemical reactions will be uncovered that obviate correlate with the perturbation of fner object level structures the need to rely on this degree of energy transduction to of molecules and atoms. Driving a prebiotic chemical system achieve the undirected, abiotic synthesis of biotic polymers. with energy powerful enough to disrupt subatomic structures Nevertheless, mapping out the relationships between object involves perturbing the highest identifable number of fne level perturbation, chemical synthesis, and energy dissipation resolution object levels possible for conditions found at indicates that these kinds of systems represent some of Earth’s surface. Tese object levels are hierarchically nested the most thermodynamically stable and robust means of and stratifed by entropy production. Each object level builds linking abiotic and biotic confgurations of matter. Systems on the levels below, while also efectively hiding details of with these attributes may have served as the progenitors the energy of the physical and chemical exchange processes of prebiotic geochemically derived automata that eventually from levels above. Te energetic and structural thresholds became living systems. that delineate these object levels provide the requirements for automata to emerge, including complex mechanistic Disclosure behaviors such as localized, periodic heat production which are critical to concentrating reactive compounds and pro- Te opinions expressed in this publication are those of the moting prebiotic polymer condensation reactions. Interstitial authors and do not necessarily refect the views of any mineral grain pore spaces provide mineral heterogeneity particular organization. Te funders had no role in study andsourcemineralabundanceonspatialscalescommen- design, data collection and interpretation, or the decision to surate with the difusion distances of RNA sequences over submit the work for publication. the half-life of phosphodiester bond hydrolysis under ideal conditions. Tese properties would indicate that such void Conflicts of Interest spaces can serve as automata memory elements prior to the emergence of a fully self-enclosed, genetically encoded cell Te authors declare that there are no conficts of interest capable of Darwinian evolution. Te mechanisms that govern regarding the publication of this paper. 18 Complexity

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