Genesis of EdenCONTENTS
QUANTUM CHEMISTRY AS THE NON-LINEAR SCIENCE OF EMERGENT COMPLEXITY
The complex expressions of chemistry particularly in biology are manifest as a final non-linear interactive consequence of cosmological quantum symmetry-breaking. The stability of the nucleus with increasing nuclear mass number and charge permits an unparalleled richness and complexity of quantum bonding structures around the diverse chemical elements. Electron-electron repulsions, spin-obit coupling, delocalized orbitals and other effects perturb the periodicity of orbital properties and lead to the development of higher-order molecular structures. Although quanta obey linear wave amplitude superposition, chemistry inherits an inverse quadtaic non-linearity in the form of the attractive and repulsive charge interactions caused by re-distributing electrons between orbital systems. Such non-linear interaction, combined with Pauli exclusion, is responsible for the diversity of chemical interaction, from the covalent bond to the secondary and tertiary effects manifest in the complex structures of proteins and nucleic acids. The quadratic nature of charge interaction, leads to a situation in polymeric chemistry akin to the Mandelbrot set, (fig 22a) and which is central in making complex molecules (fig 10) and the scale-dependent structures of tissues possible (fig 22b).
The source of this non-linear interaction is the foundation of all chemical bonding, the electric inverse square law of charge interaction. Although the state vector of a quantum-mechanical system is a linear combination of base states, exemplified by the formation of linear combinations of s & p wave functions to form the four sp3 hybrid orbitals, the electrostatic charge of the electron causes orbital interaction to have fundamentally non-linear energetics. The total energy is represented by the resonance integral of the Hamiltonian composed with the wave function, divided by the normalizing overlap integral S.
In the case of the one-electron Hydrogen molecule ion, with Saa= Sbb normalized to 1, we have 2 solutions , as indicated:
The capacity of orbitals, including unoccupied orbitals, to
cause successive perturbations of bonding energetics results in
an interaction bonding sequence, from strong covalent and ionic
bond types, through to their residual effects in the variety of
weaker H-bonding, polar, hydrophobic, and van der Waals interactions,
merging into the average kinetic energies at biological temperatures
(Watson et. al. 1988). These are responsible for secondary structures
such as the a-helix of proteins and base-pairing and stacking
of nucleic acids, and result in the tertiary and quaternary sturctures
determining the global form of large biomolecules and the globally-induced
active-site effects central to enzyme action.
2.2 Fractal and Chaotic Dynamics in Molecular Systems.
By contrast with the periodic crystalline or random amorphous
structures of most minerals, the non-periodic scale-dependent
primary, scondary and tertiary structures in proteins and RNA
that are critical to establishing the richness of their forms
and their bio-activity, fig 10. The almost unlimited variety of
monomeric primary sequences induce higher-order secondary and
tertiary structures through subsequent folding of the polymer.
These are possible only because the non-linearity of charge interaction
which causes chemical bonding also gives rise to further residual
interactions at lower energies which are resolved by cooperative
weak bonding. Proteins are powerful catalysts because the global
coherence of action arising from cooperative weak bonding makes
for very powerful and responsive active sites. Despite being genetically
coded, such molecules form fractal structures both in their geometry
and their dynamics, fig 31(e, f) (Ansari et. al. 1985, Liebovitch
et. al. 1987, 1991).
Non-equilibrium thermodynamics (Glansdorff and Prigogine 1971) and the associated oscillating chemical systems such as the Beloushov-Zhabotinskii reaction (Epstein et. al. 1983) demonstrate the capacity of auto-catalytic chemical systems, and membrane electrochemistry (Chay & Rinzel 1985), to enter into non-linear dynamics and chaos (Epstein et. al. 1983, Agladze et. al. 1984). Quantum chaos and its suppression is also an emergent issue (Gutzwiller 1992).
The prebiotic polymerizations leading to the chemical origins of life share an informational paradox in which a small number of simple reactant lead to a large array of complex interacting products with many potential catalytic interactions. The initial conditions are thus insufficient to causally determine the products, except for a few predominant products such as adenine, leading to a huge variety of possible end states with increasing complexity. This allows for a high degree of polymeric variability which can be influenced both by auto-catalytic feedback and stochastic effects.
THE NON-RECURRENT "PERIODIC" TABLE AND THE ELEMENTARY BIFURCATION TREE
Although the discrete quantum aspects of orbital occupancy are periodic, (fig 11 b, c) the properties of successive atoms in the same periods in the table are not exactly, or even approximately, periodic. Successive members of the same group differ significantly in nuclear charge, atomic radius and electron repulsion, resulting in trends which permit interactive bifurcations between their properties. For example the properties of sulphur are significantly different from oxygen, although they are a period apart. The same goes for sodium and potassium through to fluorine and chlorine. When this non-linear non-periodicity complicating the underlying periodicity of the s, p, d and f orbitals is further extended to molecular systems, the parameter space of possible interactions resembles a quantum Mandelbrot set (fig 22) forming an atlas of configurations in which the atomic interactions fig 11(a) and resulting molecular species supporting biogenesis (fig 14, 15) play a pivotal generic role.
Such trends are illustrated in polar and H-bonding properties of hydrides for which H2O is optimal (fig 11(b)), atomic and ionic radii in which the properties of elements like Na and K differ sufficiently to induce distinct H2O bonding structures, and electronegativity, fig 11(c) in which O is even more electronegative than Cl. Such partial, or quasi-periodicity is also illustrated by the intrusion of the transition element d-orbital series between the subsequent s and p series (Moeller et. al.).
The stable aspects of quantum orbital interaction in biochemical evolution can be classified into a tree of fundamental bifurcations which distinguish the elements structurally and cause divisions between their properties in interaction. This forms a generative sequence in which the bioelements have key roles (fig 11(a)). Each bifurcation gives rise to a reaction phase with added degrees of freedom and consequently greater interactive complexity. Describing the evolution of interactive chemical quantum structures in terms of funadamental force bifurcations sheds constructive light on the broad categories into which molecular free interaction differentiates and determines both the degrees of freedom and the constraints for development of interactive complexity in bio-molecules. Successive bifurcations are as follows :
3.1 Principal Bifurcation : The Covalent Interaction of
H with C, N, O.
The central covalent quantum interaction in the table of the elements
is between the two-electron 1s orbital and the eight-electron
2sp3 hybrid. This is the fundamental covalent 1-2 shell quantum
interaction and the bifurcation through which biocosmology comes
into existence. All the members of the CNO group have tetrahedral
sp3 bonding geometry and form a graded sequence in electronegativity,
from carbon in rough parity with hydrogen to electronegative oxygen,
with one and two lone pair orbitals appearing successively in
N and O. The resulting 3-D covalent bonds give C, N and O optimal
capacity to form complex, diverse polymeric structures. Symmetry
is split, because the 1s has only one binding electron state,
while the 2sp3 has a series from 4 to 7 with differing energies
and varied occupancy, as the nuclear charge increases. The 1s
orbital is unique in the generation of the hydrogen bond through
the capacity of the bare proton to interact with a lone pair orbital.
Some of the strongest covalent bonds known to chemistry are the multiple-bonds such as -CC-, -CN, and >C=O. These can be generated by applying any one of several high-energy sources such as u.v. light, high temperatures (900oC), or spark discharge to the respective atoms. Because of the higher energy of the resulting p-orbitals, these bonds possess a specific type of structural instability, in which one or two p-bonds can open to form lower energy partially s-bonded heterocyclic and other oligomeric structures. Most of the prebiotic molecular complexity generated by such energy sources can be derived from mutual polymerizations of HCCH, HCN, and H2C=O, and realated hybrids in association with 'sister' molecules such as urea H2N-CO-NH2. These include purines such as nucleic acid bases adenine and guanine, their pyrimidine complements uracil and cytosine, key sugar types such as glucose and ribose, amino acids, polypeptides, porphyrins etc. They form a core pathway from high energy stability to structurally unstable polymerization, and to complexity, which we will elucidate.
The formation of conjugated double and single bonds in these reactions results is delocalized p-orbitals (Pullman and Pullman 1962). Such orbitals in heterocyclic (N-C) rings with conjugated resonance configurations also enable lone pair n Æ p* and p Æ p* transitions (Rich and Rajbandry 1976), resulting in photon absorption and electron transfer. These two effects in combination play a key role in many biological processes including photosynthesis, electron transport and bioluminescence.
3.2 Secondary Splitting between C, N, and O : Electronegativity
Bifurcation.
In addition to varying covalent valencies, lone pairs etc., the
8-electron 2sp3 hybrid generates a sequence of elements with increasing
electronegativity, fig 11(c), arising from the increasing nuclear
charge. This results in a variety of secondary effects in addition
to the oxidation parameter, from the polarity bifurcation discussed
below, to more subtle effects such as the complementation of -CO2H
and -NH2 as generalized organic acidic and basic moieties.
Differential electronegativity results in several coincident bifurcations associated with water structure. A symmetry-breaking occurs between the relatively non-polar CH bond and the increasingly polar N-H and O-H. This results in phase bifurcation dividing the medium into polar (aqueous) and non-polar phases in association with low-entropy water bonding structures induced around non-polar molecules. This is directly responsible for the development a variety of structures from the membrane in the context of lipid molecules fig 20, to the globular enzyme form and base-stacking of nucleic acids fig 10.
Critical in this process are the optimal properties of water H2O among all molecules, making possible in turn polarity interactions, aqueous acid-base bifurcation, ionic solubility and hydrogen bonding. The optimal nature of water as a hydride is illustrated in boiling points Fig 11(b). Water provides several other secondary bifurcations besides polarity. The dissociation H2O H+ + OH- lays the foundation for the acid-base bifurcation, while ionic solubility generates anion-cation. Many key properties of proteins and nucleic acids, are derived from water bonding structures in which a counterpoint of H-bonding and phase bifurcation effects occu, determining the form of the alpha helix and nucleotide base pairing. Hydrophilic-non-polar bifurcation is central to the tertiary structures of globular proteins as 'micelles' and hairpins of RNAs, fig 10. The solubility or otherwise of a variety of molecules and ions is derived from the energies and entropies of their induced water-bonding structures. The large diversity of quantum modes in water is demonstrated by its very high specific heat, contrasting with that of proteins (Cochran 1971). Polymerization of nucleotides, amino-acids and sugars all involve dehydration elimination of H2O, giving water a central role in polymer formation.
3. Ionic Bifurcation.
The cations bifurcate in two phases : monovalent-divalent,
and series (Na´K, Mg´Ca). Although ions such as K+
and Na+ are chemically very similar, their radii of hydration
differ significantly enough to result in a bifurcation between
their properties in relation to water structures and the membrane.
Smaller Na+ and H3O+ require water structures to resolve their
more intense electric fields. Larger K+ is soluble with less hydration,
making it smaller in solution and more permeable to the membrane
(King 1978) . Ca2+ and Mg2+ have a similar divergence, Ca2+ having
stronger chelating properties. This causes a crossed bifurcation
between the two series in which K+ and Mg2+ are intracellular,
Mg2+ having a pivotal role in RNA transesterifications. Cl- remains
the central anion along with organic groups. These bifurcations
are the basis of membrane excitability and the maintenance of
concentration gradients in the intracellular medium which distinguish
the living medium from the environment at large.
4 P and S as Low-energy Covalent Modifiers.
The second-row covalent elements are sub-optimal in their
mutual covalent interactions and their interaction with H. Their
size is more compatible with interaction with O, forming e.g.
SiO32-, PO43- & SO42- ions including crystalline minerals.
The silicones are notable for their O content by comparison with
hydrocarbons. However in the context of the primary H-CNO interaction,
two new generic properties are introduced.
PO43- is unique in its capacity to form a series of moderate energy dehydration polymers, both in the form of pyro- and poly-phosphates, and in interaction with other molecules such as sugars. The energy of phosphorylation falls neatly into the weak bond range (30-60 kj/mole) making it suitable for conformational changes. The universality of dehydration as a polymerization mechanism in polynucleotides, polypeptides, polysaccharides and lipids, the involvement of phosphate in adenosine triphosphate (ATP) energetics, ribonucleic acid (RNA) and membrane structure, and the fact that the dehydration mechanism easily recycles, unlike the organic condensing agents, give phosphate optimality as a dehydrating salt.
The function of S in biosystems highlights a second optimality. The lowered energy of oxidation transitions in S particularly S-S ´ S-H , by comparison with first row elements, gives S a unique role as a mediating mild covalent linkage both in terms of tertiary bonding and low energy respiration and photosynthesis pathways.
5 Transition Element Catalysis
Transition elements add key d-orbital effects, forming a catalytic
group. Almost all of the transition elements e.g. Mn, Fe, Co,
Cu, Zn are essential biological trace elements (Frieden 1972),
promote prebiotic syntheses (Kobayashi and Ponnamperuma 1985)
and are optimal in their catalytic ligand-forming capacity and
valency transitions. Zn2+ for example, by coupling to the PO43-
backbone, catalyses RNA polymerization in prebiotic syntheses
and occurs both in polymerases and DNA binding proteins. Both
the Fe2+-Fe3+ transition, and spin-orbit coupling conversion of
electrons into the triplet-state in Fe-S complexes occur in electron
and oxygen transport (McGlynn et. al. 1964). Other metal atoms
such as Mo, Mn have similar optimal functions, e.g. in N2 fixation.
These five processes between them constitute the major quantum bifurcations in the free interaction of the elements. They are also the central processes operating in biogenesis. Put together this says the following: The central biogenesis pathways are themselves results of the central interactive quantum bifurcations of symmetry-breaking and its resulting non-linear interactions. While life may be possible from other combinations of elements and other temperatures and pressures, life as we know it has taken the sang raal or blood-royal route of quantum cosmology.
Kenso Soai (1998) and his team have demonstrated the autocatalytic
bifurcation framework as well They took a mixture of compounds
containing a small excess of one enantiomer of the amino acid
leucine. In the presence of this imbalance, the components of
the solution reacted to form a compound called a pyrimidyl alkanol,
also with a small excess of one enantiomer. But this molecule
then acted as a catalyst in its own formation, and soon almost
all the pyrimidyl alkanol in the solution was of this sort. (see
also New Sci 12 Dec 98 16)
7 Tertiary Interaction of Mineral Interface.
Both silicates such as kaolinite clays (Strigunkova et. al. 1986)
and volcanic magmas (Lavrentiev et. al. 1984) have been the subject
of intensive interest as catalytic or information organizing adjuncts
to prebiotic evolution. Clays have been proposed as a primitive
genetic system and both include adsorbent and catalytic sites
(Cairns-Smith 1982, Weiss 1981). Clays also appear to play a key
role in stabilizing ribonucleotide polymerization (Ferris 1996).
The mineral interface involves crucial processes of selective
adsorption, chromatographic migration, and fractional concentration,
which may be essential to explain how rich concentrations of nucleotide
monomers could have occurred over geologic time scales.
STRUCTURAL DYNAMICS OF THE CORE POLYMERIZATION PATHWAYS
The initial polymerizations of energetic multiple-bonded monomers in the reaction in figs 14 and 15 form a particularly interesting problem from a quantum-mechanical point of view, because they provide some of the richest examples of growth in quantum-mechanical complexity, in which a relatively small number of simpler entities give rise to increasingly complex structures whose properties cannot be fully predicted from the initial conditions.
H2C=O in aqueous solution gives rise to 4 to 7 carbon sugars, including ribose, as well as branched polysaccharides. HCN gives rise to heterocyclic purine and pyrimidine nucleic acid bases, and in addition several amino acids, polypeptides, porphyrins, and many other types of biomolecule (Lowe et. al. 1963, Calvin 1969, Mizutani et. al. 1975). A similar array of products arises from hybrids such as cyanogen NC-CN (Schwartz et. al. 1975) and cyanoacetaldehyde NC-CH2-H2C=O. Although several of these products, such as the ring polymers adenine (HCN)5 and ribose (H2CO)5 are stable product structures, many of the more complex products, such as particular oligopeptides are metastable or stochastic products of the reaction. These conditions differ markedly from the current biochemical regime in which structurally-stable metabolic pathways are maintained through genetically-coded enzyme catalysis except where recombinational stochasticity is specifically initated as in generation of antibody immuno-diversity.
Since the initial conditions do not contain sufficient information to determine the final products, the system contains many potential outcomes. The lower energy configuration of key products, such as adenine's resonance stabilization, leads to some stable conformations based on free energy. Stochastic indeterminacies in the interaction of simpler molecules lead to multiple branching pathways. Products of increasing complexity such as polypeptides possess increasingly active catalytic potential, which may alter the structural-stability of polymerization to favour certain types of product. The dynamics may trigger a sequence of autocatalytic bifurcations, some of which may result in the formation of attracting molecular products. These reaction pathways are capable of producing a vast variety of complex molecules with generic relationships to key biomolecules, including amino acids, polypeptides, HCN polymers, purines, pyrimidines and porphyrins.
Both HCN and HCHO polymerizations have prominent cyclic products which act as spontaneous end points of polymerization, because cyclization mutually neutralizes reactive moieties. The purines, pyrimidines, ribose and porphyrins all display structure consistent with being cyclic terminators. The capacity of polymers for non-periodic primary sequencing gives rise to complex tertiary structures, which are fractal as a result of structure on several overlapping scales from the atom, through local groups, to structures such as a-helices through to global conformation changes. This fractal nature is reflected both in the geometry and the quantum energetics of molecular transformations (Ansari et.al. 1985, Liebovitch & Toth 1991). Substrate form is dependent firstly on local active sites, and in turn on the global tertiary structure of catalytic molecules.
Although the first syntheses produced the purines adenine and guanine readily, cytosine and uracil, the complementary pyrimidine bases making up the other half of the pair A-U and G-C, however Stanley Miller, forty three years after his original pioneering experiment in spark synthesis, with Michael Robertson, discovered a way for the primordial pond to make them in high yield. Although urea is produced in Miller's original experimental setup, it never reaches a high enough concentration. When he added more urea, it reacted with cyanoacetaldehyde, another by-product of the spark synthesis, churning out vast amounts of the two bases. Urea would have been able to reach high enough concentrations as shallow pools of water on the Earth's surface evaporated. (Cohen 1996, Horgan 1996).
Eschenmoser (1992) has found that glyceraldehyde phosphate in the presence of HCHO will produce 5-carbon sugars with up to 33% ribose. In the absence of HCHO the reaction tends to produce 6-carbon sugars. The phosphate-induced reaction is key here because RNA, ATP and glycolysis all involve phosphate dehydration energy. This indicates a specific link to phosphate energy primordial to the formation of oligonucleotides and even ribose.