A Dissipative Photochemical Origin of Life: The UVC Abiogenisis of Adenine
PPhotochemical Dissipative Structuring, Proliferation and Evolution atthe Origin of Life
Karo MichaelianJuly 2, 2020
Department of Nuclear Physics and Application of Radiation, Instituto de F´ısica, Universidad Nacional Aut´onoma deM´exico, Circuito Interior de la Investigaci´on Cient´ıfica, Cuidad Universitaria, M´exico D.F., Mexico, C.P. 04510. karo@fisica.unam.mx
Abstract
I describe the non-equilibrium thermodynamics and the photochemical mechanisms which may have beeninvolved in the abiotic synthesis, proliferation, and complexation of the fundamental molecules of life fromsimpler and more common precursor molecules such as HCN, H O and CO under the long wavelength UVCand UVB solar photon flux prevailing at Earth’s surface during the Archean. The fundamental moleculesabsorb strongly in this UV region and exhibit strong non-adiabatic coupling between their excited and groundstates which endows them with efficient photon disipative capacity (broad wavelength absorption and rapidradiationless dexcitation) indicative of their dissipative structuring at the origin of life. Proliferation of themolecule occurs if the photochemical dissipative structuring becomes autocatalytic. Evolution occurs whena concentration fluctuation near a bifurcation becomes amplified, resulting from the non-linearity due to theautocatalicity, leading the system to a new stationary state with a different molecular concentration profile ofusually greater photon dissipative efficacy. This direction of evolution is predicted by the universal evolutioncriterion of classical irreversible thermodynamic theory established by Onsager, Glansdorff, and Prigogine. Theexample of the UV photochemical dissipative structuring, proliferation, and evolution of the nucleobase adenineis given. The kinetic equations are resolved under different environmental conditions providing the first non-equilibrium thermodynamic analysis of the photochemical structuring of adenine. keywords : origin of life; disspative structuring; prebiotic chemistry; adenine There are two coexisting classes of structures in nature; equilibrium structures and non-equilibrium structures.Equilibrium structures arise naturally and their synthesis from arbitrary distributions of material can be describedthrough the minimization of a thermodynamic potential, for example, a crystal structure arising from the min-imization of the Gibbs potential at constant temperature and pressure. The second class is of non-equilibriumstructures known as dissipative structures which also arise naturally through the optimization of the dissipationof an externally imposed generalized thermodynamic potential (1), for example the “spontaneous” emergence ofconvection cells arising to increase the thermal dissipation at a critical value of an imposed temperature gradient.Life, although incorporating equilibrium structures, is fundamentally a non-equilibrium process and therefore itsexistence is dependent on the dissipation of one or more thermodynamic potentials in its environment. Boltzmannrecognized this almost 125 years ago (2) and suggested that life dissipates the solar photon potential (3). Presentday life has evolved to dissipate other thermodynamic potentials accessible on Earth’s surface, for example, chemicalpotentials available in organic or inorganic molecules or available in gradients at hydrothermal vents. However, UVlight would have provided an approximately three orders of magnitude greater, and continuous, source of free energythan volcanic activity and electric discharge combined (4; 5; 6), irrespective of a more radioactive Archean Earth.This UV wavelength solar photon flux was continually available at Earth’s surface for over 1000 million years duringthe Archean and thus could have provided the dissipative potential for not only for molecular synthesis, but also formolecular proliferation and the evolution towards a biosphere of ever greater global photon dissipation. Furthermore,the free energy available to a precursor molecule for covalent bond transformation is orders of magnitude greater1 a r X i v : . [ phy s i c s . b i o - ph ] J un or photochemical reactions than for thermal reactions (section 3). There is,therefore, much greater rational in theconjecture that the solar photon potential, rather than some chemical potential, was responsible for the originaldissipative structuring, proliferation, and evolution of the fundamental molecules of life (those common to all threedomains).We have identified the long wavelength part of the UVC ( ∼ ∼ ∼ . +2 ) became overwhelmed by organisms performing oxygenic photosynthesis.A strong argument in favor of the conjecture that the fundamental molecules of life resulted from dissipativestructuring under this wavelength region, corresponding to Archean atmospheric transparency (figure 1), is thatlonger wavelengths do not contain sufficient free energy to directly break double covalent bonds of carbon basedmolecules, while shorter wavelengths have enough energy to destroy these molecules through successive ionizationand fragmentation. −2 −2 A d e n i n e A d e n i n e G u a n i n e G u a n i n e T hy m i n e T hy m i n e C y t o s i n e U r ac il P h e ny l a l a n i n e P h e ny l a l a n i n e T y r o s i n e T y r o s i n e T r yp t oph a n T r yp t oph a n H i s ti d i n e H i s ti d i n e L y s G l u A r g A s p T h i a m i n e T h i a m i n e R i bo f l a v i n F o li c ac i d F o li c ac i d N i c o ti n a m i d e P y r i dox i n e P y r i dox i n e U b i qu i non e P hy t o m e n a d i on e P hy t o m e n a d i on e P hy t o m e n a d i on e H yd r oxo c ob a l a m i n P y r i dox a l P y r i dox a l NAD
NAD P F M N F AD P hy t o e n e C h l o r i n S c y t on e m i n C h l o r ophy ll b P ho s pho li p i d s I s op r e no i d Q u i on e s E n e r gy F l ux [ W m − m m − ] Wavelength [nm]
Figure 1: The spectrum of light available in the UVC and UVB regions at Earth’s surface during the Archean. Thenames of the fundamental molecules of life (nucleic acids, amino acids, fatty acids, co-enzymes and co-factors) areplotted at their wavelengths of maximal absorption (the font size of the letter roughly corresponds to the relativesize of their molar extinction coefficient) and coincide with this predicted atmospheric window which existed frombefore the origin of life at approximately 3.85 Ga and until at least 2.9 Ga (curves black and red respectively). CO and probably some H S were responsible for absorption at wavelengths shorter than ∼
205 nm and atmosphericaldehydes (comon photochemical products of CO and water) absorbed between approximately 285 and 310 nm(10). Around 2.2 Ga (yellow curve), UVC light at Earth’s surface had been extinguished by oxygen and ozoneresulting from organisms performing oxygenic photosynthesis. The green curve corresponds to the present surfacespectrum. Energy fluxes are for the sun at the zenith. Adapted from Michaelian and Simeonov (12).Numerous empirical evidences also support the conjecture of the dissipative structuring of the fundamentalmolecules of life under these wavelengths. First, the maximum in the strong absorption spectrum of many of thesemolecules coincides with the predicted window in the Archean atmosphere (Fig. 1). Secondly, many of the funda-2ental molecules of life are endowed with peaked conical intersections (section 3.2) giving them a broad absorptionband and high quantum yield for rapid (picosecond) dissipation of the photon-induced electronic excitation energyinto vibrational energy of molecular atomic coordinates, and finally into the surrounding water solvent. Perhapsthe most convincing evidence of all, however, is that many photochemical routes to the synthesis of nucleic acids,amino acids, fatty acids and sugars from simple, presumably common, precursor molecules have been identifiedat these wavelengths and the rate of photon dissipation within the Archean window generally increases after eachincremental step on route to synthesis (13; 14), a behavior strongly suggestive of dissipative structuring (section 2).In contradistinction to the generally held view that UV wavelengths were detrimental to early life and therebyinduced extreme selection pressure for mechanisms or behavioral traits that protected life from, or made life tolerableunder, these photons (10; 15; 16; 17), here I argue that these wavelengths were not only fundamental to thephotochemical synthesis of life’s first molecules (as suggested with increasing sophistication by Oparin (18), Haldane(19), Urey (20), Sagan (21) and Mulkidjanian (17) and supported experimentally by Baly (22), Miller (23), Oroand Kimball (24), Ponnamperuma et al. (25; 26; 27), Ferris and Orgel (28), and Sagan and Khare (29) as wellas others) but that this UV light was fundamental to the origin and early existence of the entire thermodynamicdissipative process known as “life” comprising of synthesis, proliferation, and evolution (section 2) leading tobiosphere complexation with concomitant increases in photon dissipation over time. Rather than seeking refugeor procuring protection from this UV light, it is argued here that molecular transformations providing innovationswhich allowed early life to maximize UV exposure; e.g. buoyancy at the ocean surface, larger molecular antennasfor capturing this light, increases in the width of the wavelength absorption band, and peaked conical intersectionsproviding extraordinarily low antenna dead-times, would all have been thermodynamically selected for. Indeed,there exists empirical evidence suggesting selection for traits optimizing UV exposure for particular amino acidscomplexed with their RNA or DNA cognate codons, particularly for those amino acids displaying the strongeststereochemical affinity to their codons or anticodons (30). This has led us to suggest that UVC photon dissipationwas the basis of the initial specificity in the amino acid - codon association during an early stereochemical era (31).Life may thus be identified with a particular form of dissipative structuring; microscopic dissipative structuringof carbon based molecules under UVC light in which the synthesized products, the fundamental molecules, wereinitially UVC pigments which demonstrated stability for long periods due to their peaked conical intersections whichdramatically reduces the quantum efficiency for dexcitation through further photochemical reaction pathways.Unlike macroscopic dissipative structures such as hurricanes or convection cells, at normal temperatures thesemicroscopic dissipative structures remain intact even after the removal of the imposed light potential driving theirsynthesis due to strong covalent bonding between atoms.I will show in section 4 that if intermediate product molecules on route to the dissipative synthesis of thefundamental molecules are catalysts for the photochemical reactions, then this would lead to their proliferation,as well as to that of their final product molecules. Efficacy in dissipation will be shown to be selected for by aan established non-equilibrium thermodynamic criterion (section 2) and this, along with proliferation, provides amechanism for evolution which may be termed dissipative selection , or more generally, thermodynamic selection .Dissipative structuring, dissipative proliferation, and dissipative selection, are the necessary and sufficient elementsfor a non-equilibrium thermodynamic framework from within which the origin and evolution of life can be explainedin physical and chemical terms (7; 8; 3).The perspective taken here, therefore, is that the origin of life was not a scenario of organic material organizationdriven by natural selection leading to “better adapted” organisms, or to greater chemically stability (e.g. UVresistant organisms), but rather a scenario of the dissipative structuring of material under the imposed UV solarphoton potential leading to an organization of material in space and time (biosynthetic pathways) providing moreefficient routes to the dissipation of the externally imposed photon potential. The dissipative synthesis of an everlarger array of photochemical catalysts and cofactors, would mean that ever more complex biosynthetic pathwayswould emerge through thermodynamic selection to promote the synthesis of novel pigments for dissipating not onlythe fundamental UVC and UVB regions, but eventually the entire short wavelength region of the solar photonspectrum (12; 32), eventually reaching the red-edge ( ∼
700 nm) which is the approximate limit of biological photondissipation on Earth today.There exists many proposals, supported by a large body of empirical data, for the exogenous delivery (comets,meteorites, and space dust) or endogenous synthesis (atmospheric, ocean surface, warm ponds, hydrothermal vents)of the fundamental molecules of life. Free energy sources proposed for synthesis on Earth include; meteoric shockimpact, electric discharge, high temperature, temperature gradient, pH gradient, particle radiations, gamma rays,UV light, organocatalysis, micro forces, etc. However, a robust explanation of life requires a clear understandingas to not only how biologically important molecules spontaneously emerged, but how they proliferated and evolvedinto ever more complex macroscopic structures building a global dissipative process known as the biosphere .3Information first” theories for the origin of life inevitably decay into equilibrium since little or no attention ispayed to the dissipation of an externally imposed generalized thermodynamic potential. “Metabolism first” theoriesrecognize the need for a free energy source for synthesis and homeostasis but fail to recognize the association ofincreasing dissipation with proliferation and evolution. The thermodynamic dissipation theory for the origin of life(8; 3), employed as the framework here, assigns an explicit thermodynamic function to life; life is the dissipativestructuring, proliferation, and evolution of molecular pigments and their complexes from common precursor carbonbased molecules under the imposed short wavelength solar photon potential for performing the explicit thermodynamicfunction of dissipating this light into long wavelength infrared light (heat) . The external photon potential suppliedcontinuously by the environment, and its dissipation into heat by the spontaneously-assembled dissipative structures,are both integral parts of our definition of life.
Irreversible processes can be identified by the distribution (flow) of conserved quantities (e.g. energy, momentum,angular momentum, charge, etc.) over an increasing number of microscopic degrees of freedom, often involving,at the macroscopic scale, spatial coordinate degrees of freedom. Corresponding to a given flow there exists aconjugate generalized thermodynamic force. For example, to the macroscopic flows of heat, matter, and charge,over coordinate space, there corresponds the conjugate forces of minus the gradient of the inverse of temperature,minus the gradient of mass density (concentration gradient), and minus the gradient of the electric charge density(the electrostatic potential) respectively. Flows of the conserved quantities can occur not only over macroscopiccoordinate degrees of freedom, but also over molecular degrees of freedom, such as over electronic or vibrationalcoordinates, spin coordinates, and reaction coordinates (ionizations, deprotonations, charge transfer, disassociations,isomerizations, tautomerizations, rotations around covalent bonds, sigmatrophic shifts, etc.), obeying statisticalquantum mechanical rules. The corresponding conjugate forces to these flows of the conserved quantities involved inthe molecular processes of life are electromagnetic in nature, for example, the chemical and photochemical potentials.Since, for covalent, strongly bonded organic material, access to these molecular degrees of freedom usually requiresthe deposition of a large amount of the conserved quantity (e.g. energy) locally (e.g. on a particular region of amolecule), such flow, and any resulting dissipative structuring occurring at the origin of life (before the evolutionof complex biosynthetic pathways) was necessarily associated with ultraviolet photon absorption.The existence of any macroscopic flow, or equivalently any unbalanced generalized thermodynamic force, neces-sarily implies that the system is not in thermodynamic equilibrium. Under the assumption of local thermodynamicequilibrium (e.g., local Maxwell-Bolzmann distribution of particle velocities or excited vibrational states), Onsager,Prigogine, Glansdorff , Nicolis, and others developed the mathematical framework to treat out-of-equilibrium phe-nomena known as “Classical Irreversible Thermodynamics” (CIT) (1). In this framework, the total internal (tothe system) entropy production P per unit volume, σ ≡ P/V = ( d i S/dt ) /V , of all irreversible processes occurringwithin the volume due to n generalized thermodynamic forces k = 1 , n is simply the sum of all forces X k = A k /T (where A k are the affinities and T is the temperature) multiplied by their conjugate flows J k . This sum, by the localformulation of the second law of thermodynamics (1), in any macroscopic volume, is positive definite for irreversibleprocesses and equal to zero for reversible processes (those occurring in thermodynamic equilibrium), σ ≡ PV = d i S/dtV = (cid:88) k =1 ,n X k J k = (cid:88) k =1 ,n A k T J k ≥ . (1)The validity of the assumption of local equilibrium for the case studied here, of molecular photochemical dissipa-tive structuring of the fundamental molecules, requires that the absorbed energy of the incident photon becomesdistributed with Boltzmann statistics over the nuclear vibrational degrees of freedom implicated in molecular trans-formations (hot excited or hot ground state reactions). Note that the Franck-Condon principle implies that theelectronically excited molecule will most likely be in a vibrationally excited state. Organic materials in the liquid orcondensed phase are generally “soft materials” in the sense that their vibrational degrees of freedom in the electronicexcited state couple significantly to their vibrational degrees of freedom in the electronic ground state (unlike inthe case of inorganic material). This nonadiabatic coupling is mediated by conical intersections which allow forultra-fast equilibration of the photon energy over the vibrational degrees of freedom of the electronic ground state(see 3.2), often on sub-picosecond time scales, leaving small molecules for a short time (depending on the natureof their surroundings) with an effective vibrational temperature of 2000-4000 K. This time for vibrational equili-bration is generally less than the time required for a typical chemical transformation and therefore the irreversible4rocess of molecular dissipative photochemical structuring can be justifiably treated under the CIT frameworkin the non-linear regime. (Here, the “non-linear regime” refers to the fact that chemical - and photochemical -reactions are inherently non-linear in that the flow (the rate of the reaction) is not linearly proportional to theforce (the affinity over the temperature) except near equilibrium where affinities are small.) Indeed, Prigogine hasshown that irrespective of the imposed affinities, chemical reactions in the electronic ground state can be treatedsuccessfully under CIT theory as long as the reactants retain a Maxwell-Boltzmann distribution of their velocities,which is the case for all but very exothermic (explosive) reactions (1).The time change of the total entropy production P for any out-of-equilibrium system can be split into two parts,one depending on the time change of the forces X , and the other on the time change of the flows J , dPdt = d X Pdt + d J Pdt , (2)where, for a continuous system within a volume V , d X Pdt = (cid:90) (cid:88) k =1 ,n J k dX k dt dV , d J Pdt = (cid:90) (cid:88) k =1 ,n X k dJ k dt dV , (3)For the case of constant external constraints over the system, for example when affinities A = { A k ; k = 1 , c } areexternally imposed and held constant, CIT theory indicates that the system will evolve towards a stationary statein which its thermodynamic state variables (for example, the internal energy E , entropy S , and entropy production P = d i S/dt ) become time invariant. For flows linearly related to their forces, it is easy to show that there is onlyone stationary state and that the entropy production in this stationary state takes on its minimal value with respectto variation of the free affinities A = { A k ; k = c + 1 , n } in the system (1). This principle of minimum dissipationfor linear systems was first proposed by Lord Rayleigh in 1873 (33).However, if the flows are non-linearly related to the forces (e.g. for chemical reactions the rates of the reaction(flows) are proportional to the difference in the reactant and product concentrations, while the affinities (forces) areproportional to the logarithm of these concentration ratios), then, depending on the number of degrees of freedomand how non-linear the system is, at a certain value of a variable of the system (e.g. overall affinity), labeled a critical point , the system becomes unstable and new, possibly many, different stationary states become available,each with a possibly different value of internal entropy production P = d i S/dt . In this case, stationary states areonly locally stable in some variables of the system, or even unstable in all variables. The non-linear dynamics issuch that different stationary states, corresponding to different sets of flows J α , J β , etc. conjugate to their sets offree affinities A α , A β , etc. become available through current fluctuations δ J α , δ J β , etc., at the critical instabilitypoint (or bifurcation point) along a particular variable of the system, because, unlike in the equilibrium or in thelinear non-equilibrium regimes, in the non-linear non-equilibrium regime these microscopic fluctuations δ J α on theiroriginal flows J α can be amplified through feedback (e.g. autocatalysis) into new macroscopic flows J β (1).Since for such a non-linear system, under an externally imposed thermodynamic force, multiple stationary statesare available, an interesting question arises concerning the stability of the system and how the system may evolveover time between different stationary states. Because the system harbors critical points at which microscopicfluctuations can be amplified into macroscopic flows leading the system to a new stationary state, it cannot beexpected that there exists a potential for the system whose optimization could predict its evolution. What couldbe hoped for, however, is a statistical rule governing relative probabilities for the different evolutionary trajectoriesover the stationary states.Prigogine and co-workers have shown that, although in general no optimizable total differential (thermodynamicpotential) exists for these non-linear systems, there does, however, exist a non-total differential, the time variationof the entropy production with respect to the time variation of the free forces d X P/dt (see equation 2), which alwayshas a definite sign, d X Pdt ≤ . (4)This is the most general result so far obtained from CIT theory, valid in the whole domain of its applicability,independent of the nature of the relation between the flows and forces. It is known as the universal evolutioncriterion , or sometimes called the Glansdoff-Prigogine criterion . This criterion indicates that the free forces alwaysarrange themselves within a system such that this arrangement contributes to a decrease in the entropy production.However, in general, there is no such restriction on the total entropy production of the system because this alsoincludes a component due to the corresponding rearrangement of the flows (see Eqn. (2)) which has no definitesign. The total entropy production may either increase or decrease during evolution in the nonlinear regime,depending on the relative signs and sizes of the two terms in equation (2). In the regime of linear phenomenological5elations (a linear relation between the flows and forces), it is easy to show (1) that d J P/dt = d X P/dt and thus theuniversal evolutionary criterion, Eq. (4), correctly predicts the theorem of minimum entropy production alluded toabove, dP/dt ≤
0. The stability in the Lyapunov sense of the unique stationary state in this linear regime is thenguaranteed by the fact that the entropy production is a Lyapunov function (i.e.
P > dP/dt ≤ d X P , and the size of the catchment basins of neighboring stationarystates in a generalized phase space. For the dissipative synthesis of the fundamental molecules of life, we will seethat the size of these catchment basins is related to the number of conical intersections associated with a particularmolecular photochemical transformation and their “peakedness” (section 3), and the accessibility of these is relatedto the size of the free energy barriers on route to the conical intersections from the excited state nuclear coordinatesinitially in the Franck-Condon region (having the unperturbed ground state nuclear coordinate configuration).Even though d X P is not a total differential, it can still be used to determine the nature and local stabilityof each stationary state, not only in the linear regime as shown above, but also in the non-linear regime. Toillustrate the dissipative structuring of a fundamental molecule under UVC light and the utility of the universalevolution criterion ( d X P ≤
0) in determining probabilities for paths of evolution among multiple stationary states(distinct concentration profiles), in section 4 I present an example of the non-equilibrium thermodynamics andphotochemical kinetics of the synthesis of adenine from 5 molecules of hydrogen cyanide (HCN) (see figure 3) inwater under the impressed UVC photon spectrum of the Archean given in figure 1. Such a photochemical route toadenine was discovered experimentally by Ferris and Orgel in 1966 (28) and we have suggested that this may be anexample of dissipative structuring under a UVC+UVB photon potential (13). It will be seen how the evolution ofthe concentration profile of the intermediate molecules over different stationary states under the universal evolutioncriterion leads to an increase in adenine concentration and a concomitant increase in global photon dissipation. First,however, it is pertinent to delineate the photochemistry available to carbon based organic molecules undergoingdissipative structuring.
Absorption by an organic molecule of a visible or UV photon of the required energy E = hν leads to an electronicspin singlet or triplet excited state. The width of the allowed transition ∆ E is determined by the natural linewidth dependent on the natural lifetime ∆ t of the excited state, as given by the Heisenberg uncertainty relation∆ E ∆ t ≥ (cid:126) . In condensed material or at high pressure, further broadening occurs due to dexcitation throughcollisions with neighboring molecules, reducing further the lifetime. There is also a broadening due to the Dopplereffect which increases with temperature. Most importantly, however, for the organic molecules considered here,there is a broadening due to the coupling of electronic degrees to the vibrational degrees of freedom of the molecule(vibronic or non-adiabatic coupling).Excitation to the triplet state is a spin forbidden transition but can occur due to spin-orbit coupling or interactionwith a paramagnetic solvent molecule, for example oxygen in its spin-triplet ground state. Under laboratoryconditions and for organic molecules, however, the singlet state is favored over the triplet state by ∼ x (i.e. the dipole moment is an odd function f ( x ) (cid:54) = f ( − x )), and since an additional quantum selectionrule is that transitions must be symmetric, the symmetries of the wavefunctions of the molecule in the initial andfinal state must be different (e.g. even → odd) giving rise to the electronic angular momentum selection rule∆ l = ±
1. For example, a 1 S → S transition is forbidden while a 1 S → P transition is allowed.6 .2 Conical Intersections The Born-Oppenheimer approximation in molecular structure calculations assumes independence of the electronicand nuclear motions. However, such an approximation is obviously not valid for chemical reactions where nuclearreconfiguration is coupled to electronic redistribution and particularly not valid for photochemical reactions wherethe potential energy surface of an electronic excited state is reached.Conical intersections are multi-dimensional seams in nuclear coordinate space where the adiabatic potentialenergy surface of the electronic excited state becomes degenerate with the potential energy surface of the electronicground state of the same spin multiplicity, resulting from a normally barrier-less out of plane distortion of thenuclear coordinates (e.g. bond length stretching or rotation about a bond). A common distortion of the nuclearcoordinates for the excited state of the nucleobases is ring puckering as shown for adenine in figure 3.2. Thismulti-dimensional seam, defining the energy degeneracy, allows for rapid (sub-picosecond) radiationless dexcitationof the photon-induced electronic excited state, distributing the electronic energy over nuclear vibrational modes ofthe molecule and solvent, thereby producing entropy and leaving the molecule in the ground state ready for anotherphoton absorption event.Figure 2: Conical Intersection for adenine showing the degeneracy of the electronic excited state with the elec-tronic ground state after a UVC photon absorption event which induces a nuclear coordinate deformation known as pyrimidilization . Conical intersections provide rapid (sub-picosecond) dissipation of the original electronic excita-tion. Another common form of coordinate transformation associated with conical intersections are proton transferswithin the molecule or with the solvent. Reproduced from Andrew Orr-Ewing (34) based on Kleinermanns et al.(35) and Barbatti et al. (36)Besides providing a route for the energy dissipation in excited molecules, conical intersections also supply aroute for charge flow and thus define the photoisomerization or photoreaction products that can be reached after anexcitation event. Since conical intersections are located energetically down-hill from the Franck-Condon region, thedirection and velocities of approach of the nuclear coordinates to a conical intersection are important in definingthe outcome (37). The shape of the conical intersection seam determines the rate of dissipation and influences thefinal isomerization, tautomerization, or reaction product. For example, it is known that for the molecule retinalin rhodopsin the photoexcited molecule reaches the conical intersection extremely fast (75 femtoseconds) implyingthat the conical intersection must be peaked (inverted cone-like on the excited state potential energy surface) and,overwhelmingly, only one reaction product is reached, which for the case of retinal, as well as for the fundamentalmolecules of life, is the original ground state configuration (38). A more extended seam with different minima canlead to different reaction products (39) such as those intermediates on route to the photochemical synthesis of the7undamental molecules which will be described below. The final product in the photochemical synthesis of thefundamental molecules of life, however, always has a peaked conical intersection and therefore becomes the final and stable photoproduct of dissipative structuring in the relevant region of the solar spectrum.It has been a recurrent theme in the literature that the rapid (sub picosecond) dexcitation of the excitednucleobases due to their conical intersection had evolutionary utility in providing stability under the high flux of UVphotons that penetrated the Archean atmosphere (10; 17) since the conical intersection reduced the lifetime of theexcited state to the point where further chemical reactions were no longer very probable. However, photochemicalreactions under UVC light still do occur for the fundamental molecules of life, particularly after excitation to thelong lived triplet state, for example in the formation of cyclobutane pyrimidine dimers in RNA and DNA. Anapparently more optimal and simpler solution for avoiding radiation damage with its concomitant degradationin biological function, therefore, would have been the synthesis of molecules transparent or reflective to this UVlight. From the thermodynamic perspective of dissipation presented here, however, a large antenna for maximumUVC photon absorption and a conical intersection for rapid dissipation into heat are, in fact, the design goals ofdissipative structuring.
The photochemistry of molecules in electronic excited states is much richer than the thermal chemistry of theirground state, because; 1) the available energy conferred to the molecule by the absorbed photon allows veryendothermic reactions to occur, 2) anti-bonding orbitals are occupied in the excited state, allowing reactions tooccur that, because of electronic considerations, are prohibited in the ground state, 3) triplet states can be reachedfrom the electronic excited state, allowing for the production of intermediates that cannot be accessed in thermalreactions, 4) molecules are often converted into radicals in the excited state, making them much more reactive. Amolecule in its excited state can be a much stronger oxidizer or reductor having a pK a value substantially differentfrom that of the molecule in its ground state. For example, if the pK a value becomes more acidic, proton transferto an acceptor solvent water molecule may occur. Singlet excited states have a particularly rich chemistry, whiletriplet states have a more restricted chemistry but provide more time for vibrational equilibration. This richnessin chemistry is, in itself, yet another strong argument in favor of the complex molecules of life arising out ofphotochemical reactions at the surface of the ocean rather than, for example, thermal reactions occurring at thebottom of the ocean.Photochemical processes that arise after photon-induced excitation can be classified into dissasociations, rear-rangement, additions and substitutions. Each process constitutes a particular mechanism for molecular transforma-tion which could have been employed in the photochemical dissipative structuring of the fundamental molecules atthe origin of life under the UVC photon potential. Indeed, these mechanisms still occur today in many importantphotochemical processes of life, albeit in the visible and through much more complex biosynthetic pathways.The photochemical transformations listed above generally have a strong dependence on wavelength due to theparticular absorption characteristics of the inherent chromophores of the precursor molecules. However, it is notonly the absorption coefficient of the chromophore which is important since within a given wavelength regionthere may be two or more such molecular transformational processes in competition, and therefore the particularconformation of the electronic ground state before excitation may be relevant. This conformation could depend onthe temperature, viscosity, polarity, ionic strength and pH of the solvent, all of which are determinant in the yieldsof the final photoproducts.Some of the molecular transformations mentioned above do not belong exclusively to the domain of photochem-ical reactions but can also occur through thermal reactions at high temperature, albeit with lower yield and lessvariety of product. Therefore, some of the fundamental molecules of life could have been produced through thermalmechanisms without recourse to the incident light, for example at ocean floor hydrothermal vents. However, asemphasized in the introduction, the mere synthesis of the fundamental molecules should not be misconstrued asbeing equivalent to bootstrapping the irreversible dissipative process known as life. The continuous dissipation ofan external thermodynamic potential is a necessary condition for the structuring, proliferation, and evolution oflife, as it is for any sustained irreversible process. 8 Example: The Dissipative Structuring of Adenine
HCN is a common molecule found throughout the cosmos and its production during the Hadean and Archean onEarth was probably a result of the solar Lyman alpha line (121.6 nm) photo-lysing N in the upper atmospherewhich then attacks CH or CH to form HCN (40), or the UV (145 nm) photolysis of CH leading to a CH ∗ radicalwhich attacks N (40). HCN and its hydrolysis product formamide are now recognized as probable precursors ofmany of the fundamental molecules of life, including nucleic acids, amino acids, fatty acids (41), and even simplesugars (42; 43). As early as 1875 E. Pfl¨uger suggested that life may have followed from “cyanogen compounds” (44).The ubiquity of different chemical and photochemical routes from HCN to the fundamental molecules discoveredover the last 60 years has led to the suggestion of an“HCN World” (45; 46) occurring before the postulated“RNAWorld” (47).Figure 3: The photochemical synthesis of adenine from 5 molecules of hydrogen cyanide (HCN) in water, asdiscovered by Ferris and Orgel (1966) (28; 48). This is a dissipative structuring process that ends in adenine whichhas a large molar extinction coefficient and a peaked conical intersection at 260 nm promoting the dissipation ofphotons at the wavelength of maximum intensity of the Archean spectrum (figure 1). Four molecules of HCNare transformed into the smallest stable oligomer (tetramer) of HCN, known as cis-2,3-diaminomaleonitrile (cis-DAMN) (2), which, under a constant UV-C photon flux isomerizes into trans-DAMN (3) (diaminofumaronitrile,DAFN) which may be further converted on absorbing two more UV-C photons into an imidazole intermediate,4-amino-1H-imidazole-5-carbonitrile (AICN) (7). Hot ground state thermal reactions with another HCN moleculeor its hydrolysis product formamide (or ammonium formate) leads to the purine adenine (8). Adapted from Ferrisand Orgel (1966)(28). The synthesis of adenine from HCN has been studied by numerous groups since the first experimental ob-servations of the chemical reaction at high temperatures by Or´o in 1960 (49) and photochemically at moderatetemperatures by Ferris and Orgel in 1966 (28; 50; 51; 52; 48). Adenine is a pentamer of HCN and the overallreaction from 5 HCN to adenine is exothermic (∆ G = − . − (52)) but presents a number of largekinetic barriers which can be overcome at high temperatures or at low temperatures if UV photons are absorbed.The reactions on route to adenine are in competition with hydrolysis and UV lysis, and these relative rates aredependent on concentrations, temperature, pH, metal ion- and product- catalysis, and the wavelength dependentintensity of the incident UV spectrum. The complexities involved in the photochemical reactions leading to adeninehave been studied by Sanchez et al. (50; 51).An apparent difficulty arose with respect to the synthesis of the purines from HCN in that, for dilute concentra-tions of HCN ( < .
01 M), hydrolysis of HCN occurs at a rate greater than its polymerization, e.g. its tetramization(step 1 to 2, figure 3), the first step on route to adenine. Hydrolysis is proportional to the HCN concentrationwhereas tetramization is proportional to the square of the concentration (50). Stribling and Miller (53) estimatedthat atmospheric production of HCN and subsequent loss to hydrolysis, would have led to ocean concentrations atneutral pH no greater than about 1 . × − M at 100 ◦ C and 1 . × − M at 0 ◦ C for an ocean of 3 Km averagedepth. This led Sanchez, Miller, Ferris, Orgel (54; 50) to conclude that eutectic concentration of HCN (throughfreezing) would have been the only viable route to synthesis of the purines, and this is the primary reason whysubsequent analyses favored a cold scenario for the origin of life (55; 56; 57), not withstanding the geochemicalevidence to the contrary, and even though this severely reduces all reaction rates and inhibits diffusion.However, it is now known that the top ∼ µ m of the ocean surface (known as the microlayer) is a uniqueenvironment with the density of organic material being as large as 10 times that of bulk water below. This is due9o lowering of the free energy of fatty acids and other amphipathic molecules at the air/water interface, as wellas Eddy currents and air bubbles from raindrops bringing organic material to the surface (58; 59). Furthermore,it has been shown that even though HCN is very soluble in water (and even in non-polar solvents), it tends toconcentrate at a water surface and is observed to align itself through a dipole-dipole interaction in such a mannerso as to facilitate polymerization. Molecular dynamic simulations of HCN in water have shown that it can formpatches of significantly higher density in both the lateral and vertical dimensions at the surface, due to this ratherstrong dipole-dipole interaction between molecules (60).Our model, therefore, rather than relying on eutectic concentration to increase the solute HCN concentrationto values sufficient for significant adenine production, assumes instead the existence at the surface of fatty acidvesicles of ∼ µ m diameter which would allow the incident UVC light, as well as small molecules such as HCN,to enter relatively unimpeded by permeating its bi-layer wall (see figure 4), while trapping within the vesicle thephotochemical reaction products due to their larger sizes and larger dipole moments (table 1). This would allowthese molecules, as well as the heat of their UV photon dissipation, to accumulate within the vesicle. The existenceof hydrocarbon chains which spontaneously form lipid vesicles at the ocean surface is a common assumption inorigin of life scenarios and their probable existence during the Archean has been attributed to heat activatedFischer-Tropsch polymerization of smaller hydrocarbon chains such as ethylene at very high temperatures at deepocean vents, or to dissipative structuring under UVC photons of CO saturated water at lower temperatures onthe ocean surface (14). In order to maintain vesicle integrity at the hot surface temperatures considered here of ∼ ◦ C these fatty acids would necessarily have been long ( ∼
18 C atoms) and cross linked through UVC lightwhich improves stability at high temperatures and over a wider range of pH values (61; 14). There is, in fact, apredominance of 16 and 18 carbon atom fatty acids in the whole available Precambrian fossil record (62; 63).Figure 4: Fatty acid vesicle of ∼ µ m diameter floating at the ocean surface microlayer, transparent to UVC lightand permeable to H O, HCN and formimidic acid (Fa) but impermeable to the photochemical reaction products(e.g. ammonium formate (Af), AICN, adenine (A)).In the following subsection I present a simplified out-of-equilibrium kinetic model for our 5HCN → adeninephotochemical reaction system occurring within a fatty acid vesicle floating within the surface microlayer of a hot( ∼ ◦ C (64; 65; 66)) Archean ocean. I assume that the system is under a diurnal 8 hr flux of radiation having thespectrum presented in figure 1, including a corresponding 8 hour period of darkness during which thermal reactionsoccur but not photochemical reactions. I assume the existence of patches of relatively high concentration (0 .
01 M)of HCN and formimidic acid (Fa), a photon-induced tautomer of its hydrolysis product formamide (F), into whichour vesicle drifts periodically, and remains immersed within for short periods (120 seconds), say once every 3.5Archean days.The kinetic equations for the above model are resolved numerically, and the stationary state solutions obtained.For such a non-linear reaction-diffusion system it will be shown in section 5 that stationary state solutions existwith the highest concentration of adenine at the center of the vesicle, sufficient, in fact, to permit a subsequent UVCpolymerization of the purines into oligos after a possible UVC-assisted synthesis of ribose from similar precursor10olecules (43) and a temperature (67) or formamide-catalyzed (68) phosphorylation. A similar stationary statecoupling of reaction to diffusion, leading to regions of high concentration of the products, was shown to occur forpurely thermal reactions with different activator and inhibitor diffusion rates by Turing (69) and studied moregenerally as dissipative structures under the framework of CIT theory by Glansdorff and Prigogine (70).
Nomenclature, chemical formula, and abbreviations for the concentrations of the participating chemical species ofthe photochemical reaction leading to adenine shown in figure 3, along with their photon absorption and permeabilitydefining properties are given in table 1.Table 1: Nomenclature, chemical formula, abbreviation in the text and in kinetic equations, position in figure 3,wavelength of peak absorption (within the spectrum of figure 1), molar extinction coefficient at that wavelength,electric dipole moment and topological polar surface area (TPSA), of the molecules involved in the photochemicalsynthesis of adenine. Values marked with “??” are estimates since no data have been found in the literature.
Name chemical abbrev. abbrev. Fig. 3 λ max (cid:15) µ TPSAformula in text in kinetics nm M − cm − [D] [˚A ]hydrogen cyanide HCN HCN H 1 2.98 23.8formamide H N-CHO formamide F 220 60 (71; 72) 4.27 (73) 43.1formimidic acid H(OH)C=NH formimidic acid (trans) Fa 220 60 1.14 (73) 43.1 ??ammonium formate NH HCO ammonium formate Af +/-, 2.0 ?? 41.1diaminomaleonitrile C H N cis-DAMN (DAMN) C 2 298 14000 (74) 6.80 (75) 99.6diaminofumaronitrile C H N trans-DAMN (DAFN) T 3 313 8500 (74) 1.49 (75) 99.62-amino-3-iminoacrylimidoyl cyanide C H N AIAC J 4 275 9000 (48; 50) 1.49 99.6 ??4-aminoimidazole-5-carbonitrile C H N AICN I 7 250 10700 (74) 3.67 78.54-aminoimidazole-5-carboxamide C H N O AICA L 266 (76) 10700 ?? 3.67 ?? 97.85-(N’-formamidinyl)-1H-imidazole-4-carbonitrileamidine C H N amidine Am 250 10700 (77) 6.83 ?? 80.5 ??adenine C H N adenine A 8 260 15040 (78) 6.83 (79) 80.5hypoxanthine C H N O hypoxanthine Hy 250 12500 (80) 3.16 70.1
Under non-coherent light sources, photochemical reactions can be treated using elementary kinetics equations ofthe balance type in the product and reactant concentrations. The following chemical and photochemical reactionsmust occur in the dissipative structuring of adenine and are described in detail below.11able 2: Reactions involved in the photochemical synthesis of adenine (see figure 3). Temperature T is in ◦ K andpH is 7.0 except where noted differently. O k (cid:42) F k = exp( − . /T + 24 . − ; hydrolysis of HCN (50; 81; 82)2 γ + F → Fa q = 0 .
05 (71; 72) (83; 84; 85)3 γ + Fa → H + H O q = 0 .
03 (85; 84; 86)4 F + H O k (cid:42) Af k = exp( − . /T + 23 . − ; hydrolysis of formamide (82; 85)5 4H k (cid:42) C k = (1 . / .
0) exp( − . /T + 19 . − s − ; pH 8.2 (50)6 4H k (cid:42) T k = exp( − ∆ E/RT ) / (1 . − exp(∆ E/RT )) · k ; M − s − ; ∆ E = 0 .
61 kcal mol − (50)7 4H + T k (cid:42) C+T k = (1 . / (1 . · . − (9964 . − . /T + 19 . − s − (50)8 4H + T k (cid:42) k = k ; M − s − (50)9 γ + C → T q = 0 .
045 (74)10 γ + T → J q = 0 .
058 (74; 48; 50)11 γ + J → I q = 0 . → I ; q × q = 0 . k (cid:42) L k = exp( − ./T + 12 . − ; E a = 19 .
93 kcal mol − (51)13 I:F + Af k (cid:42) A + F k = exp( − Ea/RT + 12 . − s − ; E a = 6 .
68 kcal mol − (87; 88)14 I:F + Fa k (cid:42) Am + Fa +H O k = exp( − Ea/RT + 12 . − s − ; E a = 19 . − (89)15 γ + Am → A q = 0 .
06 (77)16 A k (cid:42) Hy k = 10 ( − /T +8 . ; s − ; valid for pH from 5 to 8 (90; 91)17 γ + C → C q = 0 . γ + T → T q = 0 . γ + J → J q = 0 . γ + Am → J q = 0 . γ + I → I q = 1 . γ + L → L q = 1 . γ + A → A q = 1 . γ + Hy → Hy q = 1 . The following is a detailed description of each reaction given in table 2:1. Hydrogen cyanide HCN (H) hydrolysis to formamide H NCOH (F) with a half-life dependent on temperatureand pH (50). The temperature dependent rate equation used here was determined by Kua and Thrush (82)at pH 7.0 from the experimental data of Miyakawa et al. (81).2. Formamide (F) can be photochemically converted through a photon-induced tautomerization into formimidicacid (Fa). Basch et al. (72) have measured the electronic excitation spectrum of formamide (F) and finda peak in absorption at 55,000 cm − (182 nm) with a molar extinction of 11,000 M − cm − . However, ashoulder exists on the main absorption peak which extends down to 40,000 cm − (250 nm). Duvernay etal. (84) suggest that this shoulder arises from the resonant excitation of the forbidden n → π ∗ transitionlocated at 219 nm (130 kcal mol − ) and not from the main π → π ∗ transition located at 182 nm. Maier andEndres (83) have determined that irradiation of formamide (F) at 248 nm rapidlly converts it into basicallytwo tautomeric isomers of formimidic acid (Fa), H(OH)C=NH, which are both about 3.6 kcal mol − in energyabove formamide and separated from it by a transition barrier of height of E a = 45 . − (gas phase).Similarly, Duvernay et al. (84) have shown that under UVC light of 240 nm, formamide (F) tautomerizes intoformimidic acid (Fa) and their calculation gives a similar transition state barrier height of 47.8 kcal mol − .Wang et al. calculate a transition state barrier of 49.8 kcal mol − (92) but show that this is reduced to to 22 . − in the presence of only a single solvent water molecule. This energy needed to overcome the barrieris in the infrared (1265 nm) but Cataldo et al. have shown that there is no evidence of thermal excitation untilabout 220 ◦ C (93). Our scenario therefore assumes that the F → Fa tautomerization requires the absorptionof a photon and we take the wavelength region for tautomerization due to the n → π ∗ transition of 220 ± − cm − as measured by Baschet al. (72) and also by Petersen et al. (71). 12. Duvernay et al. (84) have shown that formimidic acid (Fa) can, in turn, be photo-lysed into HCN (H), or HNC,plus H O (dehydration) with maximal efficiency at about 198 nm (86). However, the absorption spectrumof formimidic acid also has a shoulder extending to about 250 nm due to the same n → π ∗ excitation as informamide. For example, Duvernay et al. observe a small amount of dehydration of formimidic acid at 240nm. Given that our surface solar spectrum during the Archean (figure 1) is extinguished below about 205 nm,here we likewise assume an absorption wavelength for photo-lysing of 220 ±
20 nm and a similar average molarextinction coefficient as for the tautomerization of fomamide (F) of 60 M − cm − which is in accordance withwhat Gingell et al. (86) find. Combining photo-reactions ◦ C), thereby exciting vibrational states, a photon-induced excitation at evenlonger wavelengths (254 nm) also leads to the formation of HCN with H O, eventually leading to the purines,adenine, guanine, and hypoxanthine, and these yields are increased when including the inorganic catalystssodium pyrophosphate and calcium carbonate, indicating that heating and inorganic catalysts can improvethe photochemical reaction steps Owithout requiring the absorption of a photon, but only at temperatures greater than about 220 ◦ C (93).Figure 5: The production of formamidic acid (Fa) from formamide (F) (photoreaction ◦ C (85). The temperaturedependent rate equation given in table 2 was determined by Kua and Thrush (82) at pH 7.0 from theexperimental data of Miyakawa et al. (81). Ammonium and formate from this salt become useful for thethermal reaction leading to the final addition of an HCN (H) to AICN (I) catalyzed by formamide to giveadenine (A) (reaction x with its most stable tetramer ( x = 4) known as cis-DAMN (C)being the preferred polymer from which more complex polymers can be synthesized (93). The tetramizationof 4HCN is an exothermic thermal reaction and occurs most rapidly at a solvent pH at its pKa value, whichdecreases with increasing temperature (pKa = 8 . ◦ C and 7 . ◦ C) (50). The tetramization ofHCN into DAMN is not elementary but involves successive polymerization of HCN with H + and CN − ions(50) so is second order in the concentration of HCN. The temperature dependence of the rate of conversionof HCN to DAMN has been measured by Sanchez et al. (50). We assume transition state theory and anArrhenius equation of form, k = exp ( − E a /RT + ln A ) . (5)From the conversion rates for a 1 M solution of HCN with 0.01 M tetramer catalyst as given in table 5 ofSanchez et al. (50) a straight line can be fitted to the graph of ln(1 /T ) vs ln( k ) giving values of ln A = 19 . E a /R = 9964 .
3, or E a = 19 . − . However, this would be the rate equation for tetramerizationof HCN at its pKa value which would be about 8.2 at 80 ◦ C. At the lower pH value assumed here of 7.0, asomewhat lower rate would be indicated (50).The rates for hydrolysis and polymerization are similar for concentrations of HCN (H) between approximately0.01 M and 0.1 M (equal rates at 0.03 M for pH 7, T=80 ◦ , Fig. 15 of reference (50)). At lower concentrations,hydrolysis dominates while at higher concentrations polymerization dominates (50).6. HCN (H) can also thermally polymerize into trans-DAMN (T) which has a free energy about 0.56 kcal mol − higher than cis-DAMN (C) (75). We therefore assume that the rate constant for the polymerization intotrans-DAMN is the same as that for cis-DAMN multiplied by a temperature dependent Boltzmann factor.7. Trans-diaminomaleonitrile, trans-DAMN (T), produced through the thermal reaction groups) and acceptor parts (–CN group) linked by a double13ond. As such, it can act as a catalyst for the tetramization of 4HCN into cis-DAMN (51). Cis-DAMN isalso a catalyst for the same thermal reactions, but has significantly less activity than trans-DAMN (50) andtherefore its catalytic activity is neglected in our analysis. As can be surmised from the discussion of table7 of reference (50), including 0.01 M of the tetramer trans-DAMN increases the rate of tetramization by afactor of 12 at 20 ◦ C which would correspond to a reduction in the activation energy of 1.45 kcal mol − . Thischange in the barrier height is therefore included in the rate constant for this catalyzed reaction.8. Trans-DAMN also acts as an auto-catalyst for its own thermal production from 4HCN (51) and we assume asimilar reduction in barrier height.9. cis-DAMN can transform into trans-DAMN (3), step (2) → (3) of figure 3 through a rotation around thedouble covalent carbon-carbon bond and as such requires the absorption of a high energy photon (298 nm) toovercome the large energy barrier for rotation, calculated to be 58.03 kcal mol − (75) and > → I) has beenmeasured by Koch and Rodehorst (74) to be 0.0034. We therefore take the quantum yield of both trans-DAMNto AIAC (T → J) and AIAC to AICN (J → I) (reaction √ . → I) is taken to be √ .
034 to give the overall quantum yield for trans-DAMNto AICN (T → I) to be 0.0034 (74). AICN absorbs maximally at wavelength 250 nm.12. The imidazole, 4-aminoimidazole-5-carbonitrle, AICN (I) created in the previous photochemical reaction(reaction − and the frequencyfactor to be ln A = 12 . G = − . − , but there are numerous large energy barriers on the path to its completion(52). The first step is the coupling of an HCN molecule to AICN, and this appears to be rate limiting since ithas the highest energy barrier, calculated in the gas phase, of 39.7 kcal mol − (52). However, it is catalyzed byboth bulk solvent and specific water molecules which reduce the barrier to 29.6 kcal mol − , or by ammoniummolecules with bulk water solvent which reduce the barrier further to 27.6 kcal mol − (52). A number ofexperimental works (87; 88; 94; 85) have revealed that ammonium formate (Af) could provide a route withan even lower barrier, but the rate is still too slow to allow significant adenine production from AICN andammonium formate, unless a strong concentration mechanism existed, for example, dehydration (85), orperhaps the build up of concentration inside the vesicle, or the reaction-diffusion self-organizing occurringwithin the vesicle, as suggested here.However, as early as 1974 Yonemitsu et al. (87) showed that including formamide, the hydrolysis product ofHCN (reacction ◦ C, leading to aproposal for an industrial patent for the production of adenine from cis-DAMN (C) or trans DAMN (T) andformamide with ammonium formate. From examples 1 and 12 of the experiments of Yonemitsu et al. carriedout at 150 and 100 ◦ C (using 135 g of formamide, 30 g of ammonium formate, and 2.01 g of DAMN) givingrise to 43.5% and 30.0% product of adenine after 5 and 10 hours at those temperatures respectively, it ispossible to calculate an activation barrier for the overall reaction of E a = 6 .
682 kcal mol − . Since ammoniumformate is a salt, the probable pathway from AICN to adenine would be that proposed by Zubay and Mui (88)where the ammonium ion NH +4 attacks the triple NC bond of AICN and the formate ion HCOO − attacks theamine NH group of AICN (figure 8 of reference (88)) both catalyzed by the proton transfer process involvingformamide (see below), leading to this very low barrier. We therefore assume the reaction to be of secondorder and determined by the Arrhenius equation of form, k = exp ( − E a /RT + ln A ) , (6)14here E a = 6 .
682 kcal mol − and the pre-exponential frequency factor A was estimated from the reducedmass dependence of the Langevin model (95), A = 2 πe (cid:112) α/µ for a charged ion - neutral molecule systemwhere e is the ion electronic charge, α is the polarizability of the neutral reactant, and µ is the reduced massof the reactants (96). Considering that all factors are equal except the reduced mass and then normalizing tothe frequency factor of reaction A = 12 . ) of AICN. They show for their particular case of formiminylation of 5-aminoimidazole (Fig.13 of reference (89)) that this reaction can be formamide-catalyzed (as described above) and find the activationenergy barrier for this to be 19.9 kcal mol − (significantly lower than 46.1 kcal mol − in the noncatalyzedprocess and 34.0 kcal mol − in the water-assisted process) and that the subsequent dehydration process togive the amidine (Am) (our case) is calculated to be 14.0 kcal mol − (34.3 kcal mol − in the noncatalyzedreaction).Therefore, we assume that the attachment of HCN (H) to AICN (I) to form 5-(N’-formamidinyl)-1H-imidazole-4-carbonitrileamidine (Am) to be a formamide catalyzed thermal reaction involving formimidic acid andformamide and we assume the rate of this reaction to be determined by the Arrhenius equation of form k = exp ( − E a /RT + ln A ) (7)where E a = 19 . − and the pre-exponential frequency factor A is again estimated from the reducedmass dependence of the Langevin model (95), considering again all factors equal except the reduced mass andthen normalizing to the reaction A = 12 . − (48). This possibility will not be included inour model, but it would have the effect of increasing the rate of the production of adenine.15. After the attachment of a fifth HCN (H) to AICN (I) to form the amidine (Am), reaction − ) which, once overcome,allows the system to proceed through a subsequent barrier-less cyclicization to form adenine (77). Such ahigh barrier to the final cyclicization means that, for the temperatures considered here, it cannot be a thermalreaction. The fact that adenine has been found in space and in meteorites where temperatures are expectedto be very low indicated to Glaser et al. (77) that a photochemical route must be available. They suggesteda photon-induced tautomerization with the amidine which absorbs strongly at 250 nm. Although oscillatorstrengths for the tautomerization have been calculated by Glaser et al., different ab initio approaches givesignificantly different values and experiment will be required for its reliable determination. Therefore, until15uch data becomes available, we assume a similar molar extinction coefficient as for AICN and a quantumefficiency of q = 0 .
06, the latter being of the same order as the other photochemical reactions listed here.16. The temperature dependent rate equation for the removal of adenine (A) through hydrolysis to give hy-poxathine (Hy) which could then lead to guanine, or through deamination to some amino acids (98) wasdetermined by Levy and Miller (90), and also by Wang and Hu (91). Zheng and Meng calculated a transitionstate barrier of 23.4 kcal mol − (99).17. to 24. These reactions represent the absorption of a photon in a 20 nm region around the wavelength ofpeak absorption of the molecule which then decays through internal conversion at a conical intersection to theground state on sub-picosecond time scales. All molecules listed in this set of photo-reactions are basicallyphoto-stable, having a peaked conical intersection of the excited state with the ground state. These reactions,with large quantum efficiencies, represent the bulk of the flow of energy from the incident UVC spectrum tothe emitted outgoing ocean surface spectrum in the infrared and therefore contribute most to dissipation andentropy production.The autocatalytic nature of trans-DAMN (T) and formamide (F) in aiding in the thermal reactions, particularlyin the polymerization of HCN (table 7 of reference (50)), lead to its proliferation, and therefore also the proliferationof the final product adenine under the continuous UVC flux. The final product, adenine (8), has the greatest molarextinction and dissipative efficacy of all the intermediate precursor molecules of figure 3 within the UVC regionarriving at Archean Earth’s surface (figure 1). Inorganic catalysts have not been included directly in our reactionscheme. It has been shown, however, that inorganic catalysts increase the rate of adenine production, for exampleCu +2 ions have a large effect in increasing the rate constant for the conversion of HCN (H) to cis-DAMN (C) (50).Cu +2 ions also reduce the energy difference between the isomers (but not the barrier crossing height) formimidicand formamidic acid of formamide (100). Metal ions would have been in high abundance at the ocean surfacemicrolayer (58; 59).In order to obtain simple kinetic equations for the photochemical reactions, we assume that the molecules onlyabsorb within a region ±
10 nm of their maximum absorption wavelength λ max and that this absorption is at theirmaximum molar extinction with coefficient (cid:15) (table 1), and finally that these wavelength regions do not overlap.We assume that the vesicle is at the ocean surface and the depth coordinate is divided into i = 20 bins of width∆ x = 5 µ m and the time interval for the recursion calculation for the concentrations at a particular depth is 5 ms.The recursion relation for the factor of light intensity L λ ( i ) at a distance x ( i ) = i · ∆ x below the ocean surface willbe, L λ ( i, C ( i )) = L λ ( i − , C ( i − e − ∆ x · α λ · − ∆ x · (cid:15) λ C ( i ) (8)where α λ is the absorption coefficient of water at wavelength λ and (cid:15) λ is the molar extinction coefficient of theparticular absorbing substance which has concentration C ( i ) at x ( i ).The kinetic equation recursion relations for a time step dt and a depth bin of width ∆ x at a distance x below16he surface are determined from reactions of table 2 to be the following; dHdt = D H ∂ H∂x − k H + d · q I L ( F a ) (1 − − ∆ x(cid:15) F a )∆ x − k H − k H − k H T − k H T = D H ∂ H∂x + d · q I L ( F a ) (1 − − ∆ x(cid:15) F a )∆ x − Hk − H ( k + k + T ( k + k )) (9) dFdt = D F ∂ F∂x + k H − d · q I L ( F ) (1 − − ∆ x(cid:15) F )∆ x − k F − k IF a (10) dF adt = D F a ∂ F a∂x + d · q I L ( F ) (1 − − ∆ x(cid:15) F )∆ x − d · q I L ( F a ) (1 − − ∆ x(cid:15) F a )∆ x (11) dAfdt = D Af ∂ Af∂x + k F − k IAf (12) dCdt = D C ∂ C∂x + k H + k H T − d · q I L ( C ) (1 − − ∆ x(cid:15) C )∆ x (13) dTdt = D T ∂ T∂x + k H + k H T + d · q I L ( C ) (1 − − ∆ x(cid:15) C )∆ x − d · q I L ( T ) (1 − − ∆ x(cid:15) T )∆ x (14) dJdt = D J ∂ J∂x + d · q I L ( T ) (1 − − ∆ x(cid:15) T )∆ x − d · q I L ( J ) (1 − − ∆ x(cid:15) J )∆ x (15) dIdt = D I ∂ I∂x + d · q I L ( J ) (1 − − ∆ x(cid:15) J )∆ x − k I − k IAf − k IF a (16) dLdt = D L ∂ L∂x + k I (17) dAmdt = D Am ∂ Am∂x + k IF a − d · q I L ( Am ) (1 − − ∆ x(cid:15) Am )∆ x (18) dAdt = D A ∂ A∂x + d · q I L ( Am ) (1 − − ∆ x(cid:15) Am )∆ x + k IAf − k A (19) dHydt = D H y ∂ Hy∂x + k A (20)where d is the day/night factor, equal to 1 during the day and 0 at night. I , I , I , I and I are theintensities of the photon fluxes at 220 , , ,
275 and 250 nm respectively (Fig. 1). (cid:15) λ are the coefficientsof molar absorption for the relevant molecule and α λ are the water absorption coefficients at the correspondingphoton wavelengths λ , respectively. The permeability of the molecule through the vesicle wall and the diffusion constant of the molecule within theinner aqueous region of the vesicle will both decrease with the area of the molecule and with the size of its electricdipole moment (table 1) and increase with temperature. It is interesting to note that almost all of the final andintermediate product molecules have large dipole moments, implying their entrapment within the vesicle. Weassume that the vesicle cannot remain intact at temperatures greater than 90 ◦ C but that below this temperatureit is completely permeable to H O, HCN (H) and formimidic acid (Fa) but impermeable to all the other productsdue to their large size and large electric dipole moments. Note that ammonium formate would be in its ionic formand therefore also unable to cross the fatty acid membrane. Permeabilities across lipid boundaries are reduced byorders of magnitude if the molecules are polar or are charged (101).The diffusion constant D Y for the molecule Y will depend on the viscosity of the liquid inside the vesicle, or, inother words, on amount of organic material built up through UVC dissipative structuring within the vesicle from theprecursor molecules HCN and H O. Studies of intracellular diffusion of nucleotides indicate three factors influencingdiffusion rates besides temperature at high solute densities; the viscosity of the environment, collisional interactionsdependent on concentration, and binding interactions between molecules (102). The diffusion constant of adeninein pure water has been determined to be D A = 7 . × − cm s − (103) while the measured diffusion rates in thecytoplasm of different cell types has been measured to be between 1 . × − to 7 . × − cm s − (102).It seems likely, therefore, that, at least in some areas of the primitive ocean, there would have existed surfacefilms with a high density of trace metals, lipids and fatty acids and other hydrocarbons produced, for example, by17he same ultraviolet spectrum of figure 1 on CO saturated water (14). Diffusion in the sea surface microlayer couldthen be expected to be orders of magnitude lower than in the bulk water.Diffusion rates in our case will depend on the amount of organic material already existing at the air/watersurface captured during the formation of the vesicle, which may vary considerably. We define all diffusion constantsrelative to adenine through the formula; D Y = µ A A A µ Y A Y · D A , (21)where A A is the polar surface area of adenine (table 1) and investigate three different scenarios with diffusionconstants of three different orders of magnitude around the largest value for the diffusion constant of adenine inpresent day cytoplasm. Using the values given in table 1 for the dipole moment and the area, we obtain the resultsgiven in table 3.Table 3: Diffusion constant factors for the molecules obtained from equation 21 considering three different scenariosof D A = 1 × − , × − and 1 × − cm s − . D H D F D F a , D Af D C D T D J D I D L D Am D A D Hy Cyclical boundary conditions are assumed for diffusion, except for HCN (H) and formimidic acid (Fa) whichcan permeate the vesicle wall and therefore take on their fixed value specified in the initial conditions outside thevesicle (see below). The second order derivatives for the diffusion were calculated using 3 terms with single precisionvariables.
Miyakawa, Cleaves and Miller (81) estimated the steady state bulk ocean concentration of HCN at the origin oflife assuming production through electric discharge on atmospheric methane to produce radicals which attack N ,leading to an input rate to the oceans of 100 nmole cm − y − , and loss of HCN to hydrolysis plus a 10 million yearrecycling time of all ocean water through submarine vents for an ocean of 3 Km average depth. For an ocean of pH6.5 and 80 ◦ C, they obtained a value of [HCN]= 1 . × − M (81).However, HCN can also be produced through the solar Lyman alpha line (121.6 nm) photo-lysing N in theupper atmosphere giving atomic nitrogen which then combines with CH and CH to give HCN, or through 145nm photolysis of CH leading to a CH ∗ radical which attacks N to give HCN (40). Including this UV productionwould increase the input of HCN concentration to the oceans by a factor of at least 6 (104; 105; 53). The first ∼ µ m of the ocean surface is a unique region known as the hydrodynamic boundary layer in which surface tensionleads to enriched organics with densities up to 10 times that of organic material in the water column slightly below(58). Trace metal enhancement in this microlayer can be one to three orders of magnitude greater than in the bulk(58; 106). Langmuir circulation, Eddy currents, and the scavenging action of bubbles tends to concentrate organicmaterials into this surface film. If disturbed or mixed, the film rapidly reestablishes its integrity. This high densityof organic material trapped through hydrophobic and ion interactions at the ocean surface leads to significantlylower rates of diffusion at the surface microlayer as compared to the ocean bulk (58). Little diffusion and turbulencetherefore imply little mixing. The ocean microlayer is therefore a very stable layer which, of course, would not berecycled through ocean vents. Finally, although HCN is very soluble in bulk water, recent molecular dynamicsimulations have shown that it concentrates to about an order of magnitude larger at the air-water interface dueto lateral HCN dipole-dipole interactions, and that it evaporates at lower rates than does water (60).Therefore, rather than assuming the low bulk concentrations of Miyakawa et al., we instead consider varioushigher initial surface concentrations for HCN (H) and formimidic acid (Fa), the latter resulting from a photochemicaltautomerization of formamide, the hydrolysis product of HCN (reactions . × − M of these molecules,due to the above mentioned characteristics of the microlayer. The initial concentrations of all other reactants andproducts inside the vesicle (assumed impermeable to these) are taken to be 1 . × − M. In figures 6 through 11 I present the concentrations as a function of time in Archean days (16 hours) of the relevantmolecules in the photochemical synthesis of adenine obtained by solving simultaneously the differential kinetic18quations, (9) through (20), for the initial conditions and diffusion constants listed in the figure legend.Figure 6: Concentrations as a function of time in Archean days (16 hours) of the molecules dissipatively structuredon route to the synthesis of adenine. The initial conditions are; T=80 ◦ C, [H] = 6 . × − M, [F] = 1 . × − M,[Fa] = 1 . × − M and all other initial concentrations [ ] = 1 . × − M. The diffusion constant exponentialfactor was expn = 1 . × − (e.g. D A = 1 . × − cm s − ). There were 8 perturbations of the systemcorresponding to the vesicle floating into regions of higher HCN (H) and formimidic acid (Fa) concentrations of 0.01M for two minutes every 3.5 Archean days (as evidenced by the vertical spikes in the concentration of trans-DAMN(red line)). The yellow horizontal dashed line represents the alternate periods of daylight (yellow) and night (blank).After one Archean month, the concentration of adenine within the vesicle (black line) has grown by approximatelyfour orders of magnitude, from 1 . × − to almost 1 . × − .Figures 13 and 14 plot the concentration profile of the products as a function of depth below the ocean surfacefor the initial conditions of figure 12 at the time of 7.3 Archean days. The the coupling of reaction to diffusionleads to a non-homogeneous distribution of products, with some of these demonstrating a significant increase inconcentration towards the center of the vesicle.In table 4 I list the temperature dependence of the production of the important molecules after a 30 day periodfor different initial and boundary conditions. 19igure 7: The same as Fig. 6 except with no perturbations of the system, i.e. the system does not encounter patchesof higher concentration of HCN and Fa. The concentrations of these molecules are held constant at 6 × − and1 × − M respectively for the 30 day period. The concentration of adenine (black line) only rises to 5 . × − M over the 30 day period.Table 4: Concentrations in moles per liter M of the product molecules obtained at the given temperature and giveninitial conditions for HCN (H), formamide (F) and formamidic acid (Fa) after a 30 day period. Those labeled with“perturbation” correspond to the vesicle floating into 8 patches of 0.01 M HCN and Fa for two minutes every 3.5Archean days. T ◦ C F Fa Af C T J I Am A L Hy[H]=6E-06, [F]=1E-06, [Fa]=1E-06 M, D A = 1 . × − , perturbation80 3.907E-06 1.000E-06 5.504E-09 2.516E-06 1.614E-07 7.190E-08 9.162E-06 1.067E-10 2.384E-07 2.384E-07 1.000E-10[H]=6E-05, [F]=1E-05, [Fa]=1E-05 M, D A = 1 . × − , perturbation60 1.026E-05 1.000E-05 1.708E-08 6.379E-07 3.959E-08 1.438E-08 1.907E-06 1.000E-10 1.192E-07 7.450E-09 1.000E-1070 1.088E-05 1.000E-05 1.718E-08 1.278E-06 8.223E-08 3.739E-08 3.815E-06 1.012E-10 2.384E-07 2.980E-08 1.000E-1080 1.282E-05 1.000E-05 1.346E-08 5.076E-06 3.258E-07 1.409E-07 1.216E-05 1.069E-10 9.537E-07 2.384E-07 2.328E-1090 1.865E-05 1.000E-05 2.136E-08 1.016E-05 6.548E-07 2.905E-07 2.453E-05 1.303E-10 2.564E-06 9.537E-07 1.863E-09[H]=6E-04, [F]=1E-04, [Fa]=1E-04 M, D A = 1 . × − , perturbation80 1.028E-04 1.000E-04 6.027E-08 1.390E-05 1.725E-06 4.861E-07 2.178E-05 1.154E-10 7.629E-06 4.768E-07 1.862E-09[H]=6E-05, [F]=1E-05, [Fa]=1E-05 M, D A = 1 . × − , perturbation80 1.514E-05 1.001E-05 1.263E-08 5.079E-06 3.258E-07 1.409E-07 1.525E-05 1.145E-10 9.537E-07 4.768E-07 2.328E-10[H]=6E-05, [F]=1E-05, [Fa]=1E-05 M, D A = 1 . × − , perturbation80 1.678E-04 1.097E-05 5.386E-09 8.430E-05 5.478E-06 2.41E-06 3.910E-04 2.419E-09 7.629E-06 7.629E-06 1.863E-09[H]=6E-05, [F]=1E-05, [Fa]=1E-05 M, D A = 1 . × − , no perturbation80 1.000E-05 1.000E-05 4.768E-07 5.960E-08 1.578E-08 2.876E-09 2.378E-08 1.000E-10 5.960E-08 9.313E-10 1.000E-1090 1.000E-05 1.000E-05 9.537E-07 1.192E-07 3.498E-08 5.627E-09 1.376E-08 1.000E-10 2.384E-07 1.863E-09 2.328E-10 ◦ C. All other conditions are identical. The concentrationof adenine (black line) rises to 2 . × − M over the 30 day period.The temperature dependence of the concentrations of the product molecules after 30 Archean days is given infigure 15.In figure 16 I plot the entropy production as a function of time in Archean days due to purely photon dissipationas represented by reactions 17 to 24 of table 2. In general, the entropy production is an increasing function oftime. These photo-reactions represent the terms d J P/dt , and even though the terms d X P/dt which represent thevariation of the entropy production due to rearrangement of the affinities, are negative definite (corresponding tothe structuring of the molecules) consistent with the Glansdorf-Prigogine universal evolutionary criterion, the totalentropy production dP/dt = d J /dt + d X /dt increases due to the the fact that, as shown here, the first term whichrepresents the flow of energy through the system being converted from short wavelength into long wavelength light,increases greatly over the evolution of the concentrations of the intermediates in the system of reactions. Theproduct molecules, including adenine, have, in this sense, been dissipatively structured and should be identified as microscopic dissipative structures .In figure 17 I plot the entropy production as a function of time in Archean days due to purely photon dissipationas represented by reactions 17 to 24 of table 2 for the case in which there are no high concentration patches of HCNand Fa on the ocean surface and concentrations are kept constant at 6 × − and 1 × − respectively (i.e. noperturbation of the vesicle). Table 4 and the comparison of figures 6 and 7 clearly indicate that perturbing the system by allowing it to floatinto regions of high HCN and formimidic acid concentration provokes the system into new stationary states ofhigher product concentration, particularly for adenine. Table 4 and figure 15 also indicate that high temperaturesare important for increasing the rates of the dissipative structuring of adenine. Cold origin of life scenarios wereproposed so that eutectic concentration would increase the rate of tetramization of HCN (H) to cis-DAMN (C)with respect to the rate of hydrolysis of HCN to formamide (F) (reaction ◦ C, except with no perturbations of the system, i.e. the system does not encounterpatches of HCN and Fa, these concentrations are maintained constant at 6 × − and 1 × − M respectively forthe whole 30 day period.hydrolysis product of ammonium formate (Af) are both very important in the final step from AICN (I) to adenine(A) (reactions (cid:38) ◦ C (67; 68).Table 4 shows the final product molecule concentrations after 30 Archean days as a function of the ocean surfaceconcentration of HCN; 6 × − , 6 × − , and 6 × − M, at 80 ◦ C and different diffusion constant exponentialsof 1 × − , 1 × − , and 1 × − . These concentrations are higher than normally assumed in origin of lifescenarios and are justified on the grounds that; 1) it has been discovered that the ocean surface microlayer can haveorganic densities at 10 times larger than the bulk, implying a greater viscosity and therefore a much lower diffusionconstant for the molecules at the surface, and 2) HCN has a large dipole moment, implying ion-dipole interactionswith ions trapped in the surface microlayer. Yet another concentration mechanism for HNC may arise from thecoupling between reaction and diffusion in the non-linear regime which leads to the breaking of spatial symmetry(e.g. the Belousov-Zhabotinsky reaction (1)). The homogeneous stationary state may no longer be stable withrespect to a space dependent perturbation and intermediate products may become preferentially concentrated, andbe consumed, in a given region. We did, in fact, find this for our model, where the largest concentrations occurredat the center of the vesicle, but only significant for very low diffusion rates (e.g. D A = 1 × − cm s − , seefigures 12 and 13) and 14).The other purine, guanine, can be produced from AICA (L) (the hydrolysis product of AICN, reaction or cyanate. Cyanogen can be generated from HCN(H) either photochemically (107) or thermally (108); cyanate is obtained from cyanogen through hydrolysis (50). Theproduction of guanine from AICA would increase the entropy production of the system, as can be seen by comparingthe photon absorption characteristics of these two molecules, and would thus have been thermodynamically selected.Regarding the pyrimidines; cytosine, uracil, and thymine, Ferris, Sanchez and Orgel (109) showed that on heatingto 100 ◦ C a 5:1 ratio of cyanate with cyanoacetylene, cytosine was formed in yields of 19%. In this reaction, cytosine22igure 10: The same as Fig. 6, 80 ◦ C, except with concentrations of HCN (H) and formimidic acid at 6 × − and1 × − M.is formed mainly in a sequence involving the stable intermediate cyanovinylurea. Cyanogen or cyanoformamide canreplace cyanate in this synthesis. Since cytosine hydrolizes quite readily to uracil, and when uracil is reacted withformic acid in dilute aqueous solutions at 100–140 ◦ C, thymine is formed (110), all of the pyrimidines can therebybe obtained. These photochemical and thermal reactions, leading to the dissipative structuring of the pyrimidinesunder the same wavelength region as the purines (adenine and guanine), also occurring within a fatty acid vesicle,will be considered in a future article.
I have presented the thermodynamics and photochemical reactions involved in the dissipative structuring, prolifer-ation, and evolution of adenine as one of the fundamental molecules involved in the origin of life. More than thesimple delineation of plausible routes to synthesis of particular molecules, and more than a fortuitous structuringof these which somehow fell under the providence of selection of chemical stability, and then natural selection, theorigin of life presented here is considered as a spontaneous photochemical microscopic dissipative structuring processleading to strongly absorbing pigments with conical intersections which arise naturally to efficiently dissipate theimpressed solar photon potential. The photochemical reactions required for the dissipative structuring necessarilyoccurred in the UVC region since this region has enough energy to directly break and reform double carbon cova-lent bonds while not enough energy to disassociate these molecules. Photochemical reactions are also much morediverse than thermal reactions and include tautomerizations, dissasociations, radicalizations, isomerizations, chargetransfers, additions, and substitutions, each providing a particular mechanism which could be employed in a givenstep of dissipative structuring.For the organic precursor molecules like HCN and its hydrolysis product formamide, their conical intersectionsendow them with a significant non-adiabatic coupling of electronic degrees of freedom to nuclear vibrational degrees.At least for a short period of time, a local equilibrium of the molecules vibrational states is achieved after photonexcitation and therefore Classical Irreversible Thermodynamic (CIT) theory can be applied to these photochemical23igure 11: The same as Fig. 6, 80 ◦ C, except with the diffusion exponential two orders of magnitude smaller,1 . × − cm s − (e.g. D A = 1 . × − cm s − ).reactions occurring in either the hot excited or hot ground states.Evolution of the system is determined by two components; first, the likelihood of a microscopic fluctuationin the phase space of the internal molecular degrees of freedom which could potentially lead to a new molecularstructure, and secondly, amplification in the non-linear regime (through autocatalysis) into new macroscopic flowsof the incident energy (route of dissipation) corresponding to a new concentration profile of the products. The firstcomponent depends on the size of the “catchment basin” in the internal coordinate phase space (the shape of theconical intersection) that could lead to a new structure from the old structure. For example, if the new structurecan be photochemically synthesized from the old structure over a wide range of absorbed photon energies thenthis structure would be more probable than others only obtainable from restricted photon wavelength regions. Thesecond component is related to whether the new structure could act as a catalyst for its own production (non-linearregime). In this case, the new structure could be expected to increase its concentration, analogously to a catalyst inan autocatalytic thermal chemical reaction. Both these components foment the dissipation of the incident photonspectrum (foment entropy production) the first by presenting a broad absorption spectrum which happens to bethe case for structures presenting one or more conical intersections leading to the required reaction pathway, andthe second by increasing the flow of energy through the system due to an increase in the macroscopic amount(concentration) of such dissipative structures.I have shown, using a simple vesicle model, how adenine can be synthesized and its concentration increasedby more than 4 orders of magnitude over a relatively short period of 30 Archean days through periodic perturba-tions which lead the system to new stationary states of different product concentration with ever greater entropyproduction.This molecular evolution process of dissipative structuring from common precursor molecules under UV lightcontinues until reaching molecules with a broad absorption spectrum and which present a peaked conical intersectionalmost exclusively for internal conversion, thereby eliminating almost completely the possibility of further chemicalreactions. Such molecules with peaked conical intersections and presenting broad absorption would then forma basis set of molecules for the dissipation of photons in yet more complex compound structures. It is neither acoincidence nor a requisite of stability that the fundamental molecules of life (those common to the three domains of24igure 12: The same as Fig. 6, 80 ◦ C, except with the diffusion exponential four orders of magnitude smaller,1 . × − cm s − (e.g. D A = 1 . × − cm s − ). Six bins in depth x below the ocean surface are plotteduntil reaching the bottom of the 100 µ m (0.01 cm) vesicle. The top of the vesicle is at a depth of 0.00025 cmbelow the ocean surface. The small diffusion constant of 1 . × − cm s − allows the coupling of the reactionswith diffusion leading to spatial symmetry breaking of the concentration profiles (see figures 13 and 14) and givingthicker lines because the 6 different depth bins are plotted.life on Earth) have precisely these photochemical characteristics (figure 1) which are the “design” goals of dissipativestructuring.Dissipative structuring in biology has been ongoing, from the initial dissipation of the UVC + UVB wavelengthsin the Archean by the dissipatively structured fundamental molecules of life, to the dissipation of wavelengths up tothe red-edge by the organic pigments of today (7; 8; 12). From this perspective, evolution can be seen to have beenoverwhelmingly “concerned” with evolving complex biosynthetic pathways through this thermodynamic dissipativeselection process to produce, proliferate, and support chromophores that could dissipate ever longer wavelengths,covering an ever greater region of the solar spectrum of higher intensity up to the red-edge. The simultaneouscoupling of biotic with abiotic irreversible processes, such as ocean and air currents and the water cycle, allowed fordissipation towards still longer wavelengths beyond the red-edge (7; 111) culminating in an efficient global dissipatingsystem known as the biosphere. Such a description of biotic-abiotic complexation leading to greater dissipationis described by classical irreversible thermodynamic theory in the non-linear regime. Irreversible processes andtheir coupling occur whenever physical and chemical constraints permit it and such coupling generally reducesimpediments to greater global entropy production by introducing new microscopic degrees of freedom (112; 113; 114).There is much empirical evidence for a thermodynamic selection towards states of increased dissipation in natureon vastly different size and time scales. For example, the increase in photon absorption and dissipation efficacy of aplant leaf over its lifetime (115), the fact that ecosystem succession correlates with increasing dissipation (116; 117),and the general increase in biosphere efficacy in photon dissipation (including the plant-induced increases in thewater cycle (118; 119)) over evolutionar time. There is also evidence for this at the microscopic scale, for examplein the increase in dissipation per unit biomass of the living cell over evolutionary history (120). Here I have shownthat there exists evidence even at the nano-scale, for example, in the sequential increases in photon dissipation ateach step during the microscopic dissipative synthesis of the molecule adenine under a UVC photon potential. This25igure 13: The concentration profile of the products as a function of depth below the ocean surface (the top of thevesicle is at a depth of 0.00025 cm below the surface) for the initial conditions of figure 12 and taken at the timeof 7.3 Archean days. Six bins in depth x below the ocean surface are plotted until reaching the bottom of the 100 µ m (0.01 cm) vesicle.is an example of dissipative selection at the molecular level. It is emphasized again that this is not akin to selectionof chemical or photochemical stability because it is not related to maximizing entropy or minimizing the internalGibb’s free energy, but rather to increasing dissipation of the externally imposed photon potential, or, increasingentropy production .It could then be expected that any planet around any star giving off light in the UVC region would haveits own concentration profile of its own dissipatively synthesized carbon based fundamental molecules dependingon the exact nature of the UV environment and the precursor and solvent molecules available locally. We haveconsidered the synthesis of this basis set of molecules to be the first step of incipient life and this stage of life hastherefore already been found on the other planets of our solar system, such as the UV sulfur containing pigmentsfound in the clouds of Venus and the red chlorophyll-like pigments found on the surface of Mars and the UVCand UVB absorbing hydrocarbons found on Titan. For that matter, such molecular concentration profiles can, infact, be found in interstellar gas clouds (12). Many of these interstellar fundamental molecules which are in a gasphase rather than a solvent environment turn out to be large polyaromatic hydrocarbons (12) and this could beunderstood from the fact that without the benefit of vibrational dissipation through hydrogen bonding to solventwater molecules, these space molecules in the gas phase need to be large in size in order to have many low frequencyvibrational modes which would thereby increase dissipation. Dissipative structuring, dissipative proliferation, anddissipative selection are the necessary and sufficient elements to explain in physical-chemical terms the synthesis,proliferation, and complexation of organic molecules on planets and in interstellar space, and thus the origin andevolution of life on Earth.In summary, the results presented here suggest the following conclusions;1. The explanation for the origin of life cannot be equated with a list of scenarios for the synthesis of thefundamental organic molecules, but instead with a continuous dissipative process which allows for not onlysynthesis, but also proliferation and complexation seen in evolution, and this process, for carbon based life,26igure 14: The same as figure 13 except with an expanded y-scale for the products of lesser concentration.appears to have necessarily involved the dissipation of the UVC and UVB regions of the Archean solarspectrum.2. A model in which the fundamental molecules are produced through photochemical and thermal reactionswithin a fatty acid vesicle permeable to HCN, H O and formimidic acid (the photon-tautomerized hydrolosisproduct of HCN), but impermeable to the reaction products, allows for a significant build up of adenine andother reaction products, and would set the foundations for the beginning of cellular life.3. High surface temperatures are necessary for copious production of adenine and this is in line with the geo-chemical fossil evidence of the Archean era.4. Perturbations can lead the non-linear system into stationary states of greater product concentrations and it isreasonable to assume that these perturbations could have been caused by the vesicle floating into patches ofhigher concentration of HCN and formimidic acid existing at isolated regions of the ocean surface microlayer.5. For very low diffusion rates, there appears to be a coupling of reactions with diffusion, leading to a non-homogeneous distribution of some of the intermediate products with a significantly greater concentration ofthese in the center of the vesicle. Such symmetry breaking could facilitate further structuring like polymer-ization.6. The Glansdorff-Prigogine criterion indicating a decreasing contribution to the entropy production due tothe variation of the forces (the affinities over the temperature), is obeyed in the photochemical and thermalstructuring of the fundamental molecules. However, the total entropy production, including this structuringcomponent due to variation of the affinities, plus a second contribution due to the variation of the flowsof energy through the system, invariably increases over time. The system evolves towards final productmolecules having an absorption maximum near the peak intensity of the incident UVC spectrum and withpeaked conical intersections to internal conversion, both increasing the overall efficacy of dissipation of theincident solar spectrum. 27igure 15: The temperature dependence of the concentrations of the product molecules, with the initial conditions,[H]=6E-05, [F]=1E-05, [Fa]=1E-05 M, and all other molecules [] =1E-10 and the diffusion constant D A = 1 . × − ,with perturbations.7. The dissipative structuring, proliferation, and evolution process has continued over the evolutionary history oflife on Earth until today arriving at the red-edge ( ∼
700 nm) of the solar spectrum at Earth’s surface. Beyondthe red-edge, surface water absorbs strongly and dissipates photons efficiently. Furthermore, by fomentingthe water cycle and ocean and wind currents, the irreversible process of life has evolved to couple with otherirreversible processes, increasing further still the efficacy of solar photon dissipation into the far infrared.
Appendix: Relation to Stability Theory
In the above I have applied the CIT formalism of Prigogine, Glansdorff and Nicolis to the photochemical dissipativestructuring of adenine, one of the fundamental molecules of life, under a UVC photon potential at the ocean surface.Such an CIT analysis is sufficient to describe the synthesis, proliferation, and complexation of the fundamentalmolecules associated with the origin of life. In a non-linear system held under an imposed generalized thermodynamicforce, multiple stationary states may exist. The system, upon perturbation may evolve from one stationary stateto another. The only restriction on the direction of evolution is imposed by the universal evolutionary criterion ofGlansdorff and Prigogine which indicates that the contribution to the entropy production due to changes duringevolution of the free forces is always negative definite. There is, however, no restriction on the total entropyproduction which may either increase, decrease, or stay the same since there is another contribution to the entropyproduction due to the changes in the flows which has no definite sign. A complete stability analysis must beperformed around the stationary state, normally, linear stability analysis does not suffice. However, for chemical orphotochemical reactions, if there exist positive feedback, e.g. auto-catalysis or cross-catalysis, then the statisticaltendency will generally be towards increasing overall dissipation of the applied chemical or photochemical potentialand this has to do with the size of the catchment basins in the generalized phase space, which, in our case ofmicroscopic dissipative structuring of molecules under UV light, are related to the conical intersections connectingthe excited state to ground state for particular reaction coordinates. Only statistical probabilities for evolution can28igure 16: The production of entropy as a function of time during the photochemical dissipative structuring processleading to adenine at a sea surface temperature of 80 ◦ C. The entropy production generally increases monotonically,but not always, and although it is the Glabsdorf-Prigogine criterion, i.e. the reduction in entropy production due tothe re-arrangement of the affinities, that drives the dissipative structuring of adenine, the total entropy productionincreases due to the increase in flow of energy from the incident source at a very hot temperature (the surface of thesun) to the emitted source of low temperature (the ocean surface temperature). At night, entropy production goesto zero. Although thermal chemical reactions still occur during the night, this entropy production is not includedhere. 29igure 17: The production of entropy as a function of time during the photochemical dissipative structuring processleading to adenine at a sea surface temperature of 80 ◦ C. Without perturbation of the vesicle, i.e. it does not passthrough patches of increased HCN and Fa concentrations. The entropy production stabilizes at a value more thantwo orders of magnitude less than that of the perturbed system (figure 16).30e determined once these are delineated. Quantitatively, these will be specified by the quantum efficiencies for theparticular photochemical reaction.Since some recent works have considered general evolution of dissipative structures from a more restrictedstatistical mechanical framework using linear stability theory, here I establish the relationship between the morecomplete analysis given in section 2 using CIT theory and linear stability theory. In fact, Glansdorff and Prigoginedid exactly this comparison for chemical reactions in their 1971 book (70) and what follows here is the photochemicalanalogue of their purely chemical analysis. It is emphasized that linear stability theory is a simplified and particularcase of the CIT formalism corresponding to evolution only in the neighborhood of a stationary state and as such,contrary to what is occasionally claimed, it is not sufficient in itself to describe the evolution of a dissipative system.The the relation between the probability of a particular fluctuation occurring and entropy production was firstconsidered by Einstein (121) who showed that for a Markovian and ergodic system under Gaussian fluctuations,the probability P of a fluctuation at the equilibrium state was related to the entropy change ∆ S by P ∝ exp[∆ S/k B ] , (22)where k B is the Boltzmann constant. Since at equilibrium entropy S is maximum, ∆ S due to a fluctuation must benegative, and thus the probabilities for fluctuations which lead the system away from equilibrium towards smallerentropy become exponentially smaller with the size of the decrease in entropy. Expanding the entropy to secondorder around the equilibrium state, for small fluctuations ∆ S , gives, S = S eq + ( δS ) eq + 12 ( δ S ) eq + . . . (23)For an isolated system at equilibrium S is a maximum, so ( δS ) eq = 0, giving that ∆ S = S − S eq ≈ / δ S ) eq , andequation (22) can be rewritten P ∝ exp[( δ S ) eq / k B ] . (24)The quantity ( δ S ) eq is known as the excess entropy (due to the fluctuation) and is always negative definite (since S eq is a maximum). Since ( δS ) eq = 0 and ( δ S ) eq <
0, ( δS ) eq is a Lyapunov function and the equilibrium state isstable.This equilibrium Fluctuation Theorem was realized to also apply to non-equilibrium situations as long as thetime scales associated with the fluctuating system are much shorter than the time scales associated with changes inthe external boundary conditions. This was developed in detail by Onsager in 1931 (112; 113), and a few decadeslater by Callen and Welton (122), Onsager and Machlup (123), Kubo (124), Prigogine and Nicolis (125) and recentlyby Evans et al. (126) and Evans and Searles (127). In particular, Prigogine and Nicolis (125) made the theoremquantitative for non-equilibrium stationary states by extending Einstein’s result to give (70), P ∝ exp[( δ S ) / k B ] (25)where ( δ S ) is now calculated around a stationary non-equilibrium state. Using CIT theory it can be shown (70)that ∂∂t
12 ( δ S ) = δ X σ = 1 T Σ k δJ k δA k , (26)where δ X σ is known as the excess entropy production (due to the current fluctuations δJ k ). In this non-equilibriumcase, ( δ S ) plays the role of a Lyapunov function. The system will become unstable if processes become physicallypossible which give a negative contribution to the excess entropy production, and this can occur for autocatalyticand cross-catalytic reactions (70).Starting with ( δ S ) < ∂/∂t )( δ S ) is positive. However, for( ∂/∂t )( δ S ) negative, P will decrease. The system will then evolve to a new stationary state corresponding to amore probable state.The work of Onsager, Prigogine, and Nicolis was recently generalized by Gaspard and Andrieux (128; 129; 130;131) and given the name the “Stationary State Current-Fluctuation Theorem”. According to this theorem, theprobability P of observing a set of flows J α at the stationary state with respect to that of observing their timereversed flows − J α in the limit of large observational time t (i.e. in the time relaxed stationary state) is given by, P ( J α ) P ( − J α ) ≈ exp (cid:20) A α · J α k B T · V t (cid:21) = exp (cid:20) d i S/dtk B · t (cid:21) , f or t → ∞ , (27)31here the last term is derived from equation (1), under the assumption of local equilibrium, and is just the ex-ponential of the entropy production divided by the Boltzmann constant k B times the time t . Therefore, giventhe possibility of two (or more) sets of flows J α , J β , ... corresponding to two (or more) sets of free affinities A α , A β , ... leading to two (or more) different values of the entropy production, in the non-linear regime where multiplestationary states are possible, current fluctuations which lead the system towards the state of greater dissipationare generally favored over time for amplification and this statistical rule for the selection of stationary states ofdissipative systems we have termed thermodynamic selection (7; 8; 3) but we will use the term dissipative selection here in order to emphasize its origin, i.e. statistical selection of the configuration of greater dissipative efficacy.As with the Fluctuation Theorem, the Current-Fluctuation Theorem is not limited in its validity to macroscopicsystems (the thermodynamic limit) nor is it limited to systems in local equilibrium. Local thermodynamic equilib-rium is required only to validate the concept of entropy density in non-equilibrium situations and thus to associatedissipation with entropy production (the last term of Eq. (27)). Acknowledgments
The author is grateful to Carlos Bunge and Iv´an Santamar´ıa-Holek for their revision of, and suggestions on, themanuscript and for the financial support of DGAPA-UNAM project number IN104920.
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