Introduction

The ubiquitous homochirality of biological molecules has puzzled and intrigued scientists and laypersons for generations. Its obvious interest and importance has motivated a vast literature on the whys, hows, mechanics and philosophical implications of the fact of biological homochirality, and some of the multifarious schemes that have been proposed to explain its emergence are reviewed in Plasson et al. (2007), Blackmond (2011) and Ruiz-Mirazo and Briones (2014). Life on earth uses exclusively the D-enantiomer of ribose, the sugar moiety of the ribonucleic acids, and the L-enantiomers of the chiral amino acids. In Ball and Brindley (2014) and in parallel papers to this one (Ball and Brindley 2015a, b) we have developed and tested the hypothesis that hydrogen peroxide was both the power source and agent for change in the pre-cellular RNA world, through its role as the THP (thiosulfate-hydrogen peroxide) oscillator providing the essential periodic thermal and pH drive. Here we focus on the structure and properties of hydrogen peroxide and review some of its pertinent physical properties in relation to its direct physicochemical role as an agent for the emergence and evolution of a living RNA world. In particular we propose that its chirality may have led to homochiral amplification of D-ribonucleic acids and extinction of the L species. This brief preliminary Report is purposely speculative and presents only preliminary results, intended to stimulate experimental studies to complement detailed mathematical and computational modelling work, currently underway in our group, aimed at elucidating in depth the processes described here. Since the context of our work is the pre-cellular RNA world, we focus on the ribonucleic acids rather than the amino acids.

Our key emphasis is that hydrogen peroxide is chiral in structure, too. It is the simplest such molecule, exhibiting axial chirality due to trans and cis potential barriers to internal rotation (Hunt et al. 1965), and thus existing as a pair of non-superimposable mirror images.Footnote 1 In normal bulk phase it occurs as a racemic mixture of the enantiomeric pair P (plus) and M (minus), which are represented in Fig. 1.

Fig. 1
figure 1

Projections of 3-dimensional structural representations of the M (left) and P (right) enantiomers of hydrogen peroxide. 𝜃 is the bond angle, ϕ is the dihedral angle or angle between the two HOO planes. Inset: A model for the P enantiomer, which we fabricated, assiduously, in the office from a paper clip; its image reflected in the framed oval mirror is the M enantiomer, and a telltale shadow, just visible, in both cases betrays the out-of-plane OH bond

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There is also a high-quality literature concerned with the chirality of hydrogen peroxide, albeit exiguous. One strand involves fundamental theoretical studies of chiral discrimination in hydrogen-bonded (h-bonded) complexes of hydrogen peroxide with another chiral molecule (Dong et al. 2005; Du and Zhou 2006; Yin et al. 2009; Zhang et al. 2009). As reported by Churakov et al. (2009), crystals of L-serine perhydrate were prepared in which only one hydrogen peroxide enantiomer co-crystallized. These studies provide important evidence that hydrogen peroxide may interact enantiospecifically, but non-covalently, with chiral molecules in general. Experimental studies in which chiral organic peroxides were used for enantoselective epoxidations (Hoft 1993; Bunge et al. 2009; Bunge et al. 2013) provide evidence that covalent bonding interactions of chiral molecules with hydrogen peroxide can be enantiospecific and enantioselective.

Following Blackmond (2011), we define the enantiomeric excess ϕ for ribonucleotides and ribonucleic acids as

$$\phi=\frac{[\text{D}]- [\text{L}]}{[\text{D}]+[\text{L}]} $$

where the brackets denote concentrations. In this work we assume a symmetry-broken supply, i.e., \(\phi _{\text {supply}}\rightarrow 0^{+}\), and in “Through the Looking-Glass” section we outline a mechanism whereby ϕ may increase monotonically to 1, mediated by localised chiral microenvironments, illustrate a simplified version of the mechanism through a reinterpretation of the Frank (1953) model, and describe some of the flaws and pitfalls of dynamical system modelling of enantiomeric excess growth. In “The Medium is the Message” section we review relevant physical properties and discuss the possible effects on and consequences for the RNA world, and in “Summary and Outlook” section we summarize and anticipate work currently under way.

Through the Looking-Glass

To our knowledge enrichment of P or M enantiomers of hydrogen peroxide (Fig. 1) has not been achieved, or even attempted, in the bulk. This is because the activation energy for interconversion via the trans configuration is only 4617.6 J/mol (Hunt et al. 1965); it follows from the Boltzmann distribution that at 300 K 16 % of the population has energy greater than this, and the average energy of thermal fluctuations \(\left <\delta E\right >=\sqrt {C_{\text {v}} k_{b}N_{A}T^{2}}\approx 7400\) J mol −1, where C v is the constant-volume molar heat capacity, k b is the Boltzmann constant, and N A is Avogadro’s number. It is unlikely, too, that enantiomeric enrichment could be achieved at low temperature, because the quantum tunnelling time for interconversion is only 3 × 10−12 s (Bitencourt et al. 2008). Both thermal and quantum interconversion are expected to be effectively quenched when hydrogen peroxide forms tightly h-bonded complexes with other species and itself (Gao et al. 2010).

A racemic medium will be unable to enrich D or L nucleic acids in the bulk, but locally significant excesses of one hydrogen peroxide enantiomer are likely to occur, due to enantiopspecific interactions with the ribonucleotides and with itself (Alkorta et al. 2006). The hypothesis we develop here is based, with good supporting evidence, on the following assumptions:

  1. 1.

    A marginal excess of D-nucleotide precursors is fed to the system, due to some unspecified environmental asymmetry, which gives rise to a marginal excess of D-ribonucleic acids over L-ribonucleic acids, and chain length distributions with a small bias to D-chains of longer mean length than L-chains.

  2. 2.

    D and L species can interact via enantiomeric cross-inhibition of polymerisation (and therefore replication), as was shown experimentally by Joyce et al. (1984).

  3. 3.

    D- and L- ribonucleic acids experience localised enantiomeric excesses of hydrogen peroxide.

  4. 4.

    Effects of hydrogen peroxide on ribonucleic acids may be indirect, via conformational changes associated with h-bonding, and direct, via chemical oxidation.

Indirect Effects

The 2′-hydroxyl group is the key determinant of structure, function and reactivity of RNA (Acharya and Chattopadhyaya 2002; Fohrer et al. 2006). It is a crucial contributor to cooperative networks of hydrogen bonds (h-bonds) which stabilize helical secondary structure and folds such as tetraloops that are important for ribozyme activity. Since hydrogen peroxide is a stronger proton donor than water (Martins-Costa and Ruiz-López 2013), we propose that enantiospecific displacement of inter- or intramolecular proton donors by hydrogen peroxide at the 2′-hydroxyl group can disrupt RNA structural motifs.

Dong et al. (2005) obtained two pairs of optimized enantiomeric structures for h-bonded R and S lactic acid complexes with hydrogen peroxide, RP, SM, RM and SP, of which the significantly more stable pair was found to be RP and SM. By analogy, we propose that similar nucleotide complexes are DP, LM, DM and LP, and the more stable complexes are DP and LM. (This choice is arbitrary until settled by experiment.)

The L-ribonucleic acids are more destabilized by this chiral interaction than the D-ribonucleic acids, because the mean L-chain length is shorter, they are more likely to occur as single strands, and the L-2′-hydroxyl group is more likely to be exposed and less likely to be structurally protected. The D-ribonucleic acids are less susceptible, because the mean D-chain length is longer and the consequent greater capacity to form tightly h-bonded secondary structures would tend to protect the 2′-hydroxyl group.

Direct Interaction

There is strong experimental evidence that oxidation of nucleotides by hydrogen peroxide can occur directly, rather than by free OH radicals (Hofer 2001; Martins-Costa and Ruiz-López 2013). Thus it is reasonable to suppose that it can react enantiospecifically with ribonucleic acids.

With a greater fraction of L-chains over D-chains destabilized by indirect interaction, hydrogen peroxide can then ‘go in for the kill’, with one enantiomer (let us say M) preferentially oxidizing L-chains. Here we invoke the analogy of enantioselective epoxidations with chiral peroxides (Hoft 1993; Bunge et al. 2009; Bunge et al. 2013).

Of course, the shorter side of the D-chain distribution is also more destabilized and oxidised than the longer side, and the longer side of the L-chain distribution is better able to protect itself than the shorter side. But overall the process works in favour of increasing the average length of D-chains, up to a limit determined by thermal and pH cycling (Ball and Brindley 2015a), and decreasing that of L-chains.

The fraction of D-species increases over time, too, as well as the average length. However, the fraction of their enantiospecific reagent, P hydrogen peroxide, does not change! This gives rise to a subtle reinforcement effect: Since the racemic mixture persists in the bulk, due to facile P-M interconversion, the fraction c D/c P increases while the fraction c L/c M decreases over time. When ϕ = 1 the destructive risk posed by hydrogen peroxide to a homochiral RNA world may be reduced by up to 50 %, in principle, over that to a racemic RNA world. Although in reality this reduction would be lower, it would still be > 0. We see that as ϕ increases the RNA world becomes fitter with respect to its environment.

Thus emergence of homochirality in itself confers a significant advantage on replicating RNA species in a peroxide-mediated RNA world.

Modelling the Growth of Chirality from a Small Enantiomeric Excess

In terms of the well-known Frank model (Frank 1953) for development of a homochiral molecular system from a nearly racemic mixture, and many of its generalisations (e.g., (Kondepudi and Nelson 1984; Gutman et al. 1988; Gutman 2014)), the chiral interactions of nucleotides with hydrogen peroxide can be interpreted as reinforcing kinetically the effects of cross inhibition, thus accelerating the evolution of homochirality. Intuitively, any process that hastens homochiral development, especially in the early stages, is advantageous because there is more scope for the system dynamics to outpace large, rare fluctuations. This problem of large, stochastic fluctuations has been studied in the context of predicting times to population extinctions (Drummond et al. 2010; Ovaskainen and Meerson 2010). In a developing chiral system such fluctuations might otherwise keep the system see-sawing between relatively small D and L enantiomeric excesses.

Following Frank (1953) we assume that L and D enantiomers are produced autocatalytically from an infinite reservoir of non-chiral reagent. We assume further that L species are inactivated by the M enantiomer of hydrogen peroxide and D species are inactivated by the P enantiomer. We propose that the inactivation rate constant for L depends on the concentration of D, and that for D depends on the concentration of L. A physical argument for this effect is that since D is not affected (or less affected) by M it is more available to enhance the rate of inactivation of L by antagonism, and similarly, since L is less affected by P it is more available to enhance the rate of inactivation of D. This ‘toy’ reacting system is described as follows:

$$ \mathrm{A} + \mathrm{D} \overset{k_{1}}\rightarrow \mathrm{2D}\quad\quad\mathrm{A} + \mathrm{L} \overset{k_{1}}\rightarrow \mathrm{2L} $$
(1)
$$ \mathrm{L} + \mathrm{M} \overset{k_{2}(\mathrm{D})}\rightarrow \mathrm{Z}\quad\quad\mathrm{D} + \mathrm{P} \overset{k_{2}(\mathrm{L})}\rightarrow \mathrm{Z}, $$
(2)

where A is the non-chiral reagent, available in large excess, and Z is the inactivated product. The evolution of L and D is described by the following dynamical system:

$$ \frac{\mathrm{d}[\mathrm{D}]}{\mathrm{d}t} = {k_{1} [\mathrm{A}][\mathrm{D}]} - k_{2}{[\mathrm{P}][\mathrm{L}][\mathrm{D}]} = k^{\prime}_{1}[\mathrm{D}] - k_{2}^{\prime}{[\mathrm{L}][\mathrm{D}]} $$
(3)
$$ \frac{\mathrm{d}[\mathrm{L}]}{\mathrm{d}t} = {k_{1} [\mathrm{A}][\mathrm{L}]} - k_{2}{[\mathrm{M}][\mathrm{D}][\mathrm{L}]} = k^{\prime}_{1}[\mathrm{L}] - k_{2}^{\prime}{[\mathrm{D}][\mathrm{L}]}, $$
(4)

where the inactivation rate constant k 2 has first order dependence on D or L, and the chiral forms P and M are in large excess and remain statistically equal in concentration due to rapid thermal interconversion. The enantioselective effects are present, but subsumed in the effective rate constant \(k_{2}^{\prime }\). The solution of Eqs. 3 and 4 can be found explicitly as

$$ \mathrm{[D]}(t)= [\mathrm{D}]_{0}([\mathrm{D}]_{0} - [\mathrm{L}]_{0})([\mathrm{D}]_{0}-[\mathrm{L}]_{0}Q)^{-1}e^{k_{1}^{\prime} t} $$
(5)
$$ \mathrm{[L]}(t)=[\mathrm{L}]_{0}([\mathrm{D}]_{0} - [\mathrm{L}]_{0})([\mathrm{D}]_{0}-[\mathrm{L}]_{0}Q)^{-1}Qe^{k_{1}^{\prime} t}, $$
(6)

where

$$Q\equiv \exp\left[-\frac{k_{2}^{\prime}}{k_{1}^{\prime}}\left([\mathrm{D}]_{0}- [\mathrm{L}]_{0}\right)e^{k_{1}^{\prime} t}\right] . $$

(In writing (5) and (6) we have assumed an initial enantiomeric excess of D, D0 > L 0.) Equations 5 and 6 tell us that for any enantiomeric excess of D, no matter how small, \(\underset {t\rightarrow \infty }{\lim } \mathrm {L}(t) =0\). We also see that the larger the localised concentrations of M and P hydrogen peroxide, subsumed in \(k_{2}^{\prime }\), the faster L \(\rightarrow 0\).

We emphasize that the (Frank 1953) model and most of its variants including this simple model have heuristic value only, and show little verisimilitude to a real, experimentally accessible process. For one thing, Eqs. 5 and 6 predict \(\underset {t\rightarrow \infty }{\lim } \mathrm {D}(t) =\infty \)! Nevertheless, the model is a useful starting point for more realistic modelling of the enantioselective effects of hydrogen peroxide on the early RNA world, currently underway by our group. This will include modelling enantioselective interactions of hydrogen peroxide with a polymerising RNA system, under the periodic thermal drive provided by the THP oscillator. Viedma and Cintas (2011) found that a homochiral solid phase emerged in boiling solutions containig a racemic mixture of chiral crystals, due to dissolution-crystallization cycling under a thermal gradient. An alternative cycling model has been proposed by Ribó et al. (2013), in which reactant flow circulates between two compartments, each maintained at a different constant temperature and within which, respectively, enantioselective and non-enantioselective reactive processes are enabled. These results suggest that the thermal cycles provided by the THP oscillator may play a role in inducing localised enantiomeric excesses of M and P hydrogen peroxide.

However, it is well to proceed cautiously, because more sophisticated dynamical models for enantiomeric enrichment can be structurally unstable, implying that they either contain some pathology or that they are missing important physics. As shown in Ball (2000), Ball (2001), and Ball and Haymet (2001) and references therein, this problem unfortunately is rather frequent in dynamical models for widely different systems. This makes it impossible to determine if different models, which appeal to the same physical phenomena (symmetry-breaking and enantiomeric enrichment, in our case), belong to the same qualitative universality class even though they may differ quantitatively, as is reasonably expected. Some earlier authors have derived dynamical models for enantiomeric enrichment, which are claimed to contain the symmetry-breaking pitchfork bifurcation (e.g., Ribó and Hochberg (2008)). Yet the pitchfork is a degenerate bifurcation, which is non-persistent to perturbation. The defining and non-degeneracy conditions for the pitchfork (which are not satisfied by equations 8 and 9 of Ribó and Hochberg (2008)) are given by Ball (2001)

$$ G=G_{x}=G_{xx}=G_{\lambda}=0, \quad G_{\lambda x}\neq 0, \quad G_{xxx}\neq 0, $$
(7)

where G is the bifurcation equation for the steady states of the dynamical system, obtained in terms of a selected state variable x (sometimes implicitly), the bifurcation parameter of choice λ and the other parameters of the system. The normal form for the pitchfork — i.e., the simplest bifurcation equation that satisfies conditions (7), is

$$ G(x,\lambda)= \pm x^{3} \pm \lambda x . $$
(8)

It can be seen that any system containing a pitchfork must contain an effective cubic nonlinearity. However, Eq. 8 is degenerate, and structurally fragile to small perturbation. Two more parameters are needed to unfold it smoothly. A universal unfolding of the pitchfork is given by

$$ G(x,\lambda,\alpha,\beta)= x^{3}-\lambda x + \alpha + \beta x^{2}. $$
(9)

The parameter α is symmetry-breaking and its sign will determine the sign of x towards which the pitchfork will dissolve. In any model of a real dynamical system that contains a pitchfork α must always be nonzero (Ball 2001). The parameter β is the coefficient of the quadratic term in Eq. 9 and it tells us that the hysteresis bifurcation must also be present. In Fig. 2 are sketched the twice-degenerate pitchfork (centre), the four qualitatively distinct bifurcation diagrams of the universal unfolding (9), and the two partial unfoldings. (A miror-image set of bifurcation diagrams may also be constructed.) If we interpret Eq. 9 as the normal form corresponding to the right hand sides of a dynamical model for enantiomeric enrichment of x, where is x identified with the enantiomeric excess ϕ, the bifurcation diagrams in Fig. 2 suggest some potentially interesting scenarios. The racemic state is x = 0 but in all physical situations α is nonzero (but small) and symmetry is broken. In the top left and lower right bifurcation diagrams the symmetry-broken steady states (±x, λ) must undergo an abrupt jump to a highly non-racemic — but not necessarily homochiral — state at a turning point when the system is still only marginally non-racemic. If, at this upper steady state, the parameter λ continues to increase quasistatically, the system continues to become more highly non-racemic, and homochirality is possible. The bifurcation diagrams top right and lower left of Fig. 2 disallow jumps to high non-racemic states at a stability change — but they do permit collapse of a highly non-racemic state to an almost-racemic state! We emphasize that in a system for which the highest order steady-state singularity is a pitchfork, the bifurcation diagrams in Fig. 2 illustrate all of the qualitatively distinct behavours of which it is capable.

Fig. 2
figure 2

The four qualitatively distinct bifurcation diagrams from the universal unfolding of the pitchfork Eq. 9 — top left, top right, bottom left, bottom right. The bifurcation diagram for the pitchfork normal form Eq. 8 is shown centre, flanked left and right by the two partial unfoldings

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In a structurally stable model for symmetry-broken evolution of enantiomeric excess, the parameter λ may be qualitatively equivalent to a flow coefffcient, bringing reactants into a reacting volume and taking reactants and products out of the volume. (The diagrams may be translated into the positive realm by appropriate transformations.) The parameter α may be identified with a symmetry-broken enantiomeric excess ϕ f brought in by the flow. β is the rate coefficient for a quadratic term. The coefficient of the cubic term is subsumed into λ, α and β. Cubic nonlinearities can occur in chemical systems (e.g., Ball and Haymet2001), but they can be rather artificial, requiring two-timing assumptions on some of the chemical rate terms to be incorporated into the model, and they tend to dissolve in a more detailed treatment.

In our experience, the simplest physical mechanism for obtaining an effective, robust cubic nonlinearity that fulfils the conditions (7) is to incorporate an enthalpy balance so that the temperature becomes a dynamical variable, coupled to the concentrations via the Arrhenius temperature-dependence of the rate constants (Ball 2001; Ball et al. 2004). The enthalpy balance is coupled to a heat bath at constant temperature and the specific heat and reaction enthalpies, to a good approximation, are constant. The extreme nonlinearity of the exponential temperature dependence of the reaction rates elicits the pitchfork (and higher order bifurcations) under relatively mild conditions. In such systems, there are, also, in most cases, Hopf bifurcations present, which could make for interesting interpretation! The price is greater computational and benchmarking difficulty, but we feel the result would be more natural, since it does not require artificial cubic chemistry and a temperature-varying environment would be the norm for the RNA world — we must presume it did not grow and prosper at 298 K exactly, always.

Detailed modelling and simulations are underway in our group, as intimated above, of the role of hydrogen peroxide in the development of enantiomeric excesses of nucleic acids based on the principles outlined here of ensuring the structural stability of the model and using the temperature as a dynamical variable.

The Medium is the Message

The philosopher Marshall McLuhan (http://en.wikipedia.org/wiki/Marshall_McLuhan) proposed that society is affected by the intrinsic properties of a medium, rather than by the information the medium carries. ‘Medium’ is understood in a broad sense; here the medium is hydrogen peroxide in solution and the ‘society’ on which it operates is the RNA population. In this section we discuss how the physical properties tabulated in Table 1 may have helped to structure the RNA world, considering the entries in ordered point form:

  • Phase equilibrium and colligative effects:

    The freezing point depression ΔT f and boiling point elevation ΔT b adds to that induced by other solutes present, since

    $${\Delta} T_{\text{f}} = K_{\text{f}} (m_{1} + m_{2} +{\ldots} + m_{n}) \quad \text{and} \quad {\Delta} T_{\text{b}} = K_{\text{b}} (m_{1} + m_{2} +{\ldots} + m_{n}), $$

    where K f and K b are the respective constants and m 1 … m n are solute molalities. We may envisage hydrogen peroxide as playing a more-or-less significant part in broadening the temperature range of the liquid phase for the RNA world.

    The decrease in vapor pressure with increasing hydrogen peroxide concentration indicates a considerably lower volatility than that of pure water, as does the higher heat of vaporization. These properties may effect a concentration mechanism.

  • Density:

    Coupling between the Soret effect and convection, proposed by Mast et al. (2011) as a mechanism for concentrating ribonucleotides and RNA and driving polymerisation of longer chains, may be affected by the higher density of hydrogen peroxide solutions in opposing ways:

    • Since the particle thermophoretic velocity is inversely proportional to the fluid density ρ(T) (Brenner and Bielenberg 2005), thermophoresis would be slowed.

    • In the dynamic thermochemical environment proposed in Ball and Brindley (2015a), thermal cycling and concentration fluctuations of hydrogen peroxide could manifest as relatively strong density gradients. Since the driver of thermophoretic motion is actually the density gradient (Brenner and Bielenberg 2005), thermophoresis would be enhanced.

  • Viscosity and surface tension:

    A small surfactant effect of hydrogen peroxide may provide a a favourable environment for vesicles or proto-cells to form, given a supply of phospholipids or simpler amphiphiles. Increased visosity is likely to encourage vesicle division in a dynamic environment, due to shear stresses (Zhu and Szostak 2009). The effects would be small, but the advantages of enclosure within a semi-permeable membrane are so great for biological molecules and processes that selection pressure would be strong to evolve catalytic replication, and reduce reliance on thermochemical cycling to melt double-stranded RNA (Ball and Brindley 2014), which would tend to disrupt primitive membranes.

    Thus, the dynamic presence of hydrogen peroxide can effectively prepare the RNA world for continued existence and evolution as the supply diminishes.

  • Electrical properties:

    Relative permittivity data for hydrogen peroxide solutions are very interesting indeed, with respect to chiral discrimination, because this property shows a maximum that shifts to higher concentrations with decreasing temperature as shown in Fig. 3. This anomalous maximum was attributed to enhanced structuring of water (Gross and Taylor 1950), but in the light of more recent quantum mechanical calculations (Alkorta et al. 2006) it may be due more to the aggregation of homochiral and heterochiral clusters. From these data, using the Debye equation and assuming constant density, we can calculate the mean dipole moment of a 0.5 mole fraction solution as μ≈6.0 D. While, strictly speaking, the dipole moment is a molecular property, this result does provide evidence that hydrogen peroxide solutions are more polar, h-bonded, and highly structured than pure water, especially given that the computed dipole moment for unstructured hydrogen peroxide in solution is only 2.56 D (Table 1). Enantiospecific interactions with the 2′-OH group of the ribonucleotides would tend to stabilise homochiral clusters and provide the localised chiral environment that leads ulimately to D-amplification.

Table 1 Relevant physical properties of hydrogen peroxide, solutions and pure (wt%), compared with those for pure water (second column) (Schumb et al. 1953; Gubskaya and Kusalik 2002; Martins-Costa and Ruiz-López 2013; McGrath 2015)
Full size table
Fig. 3
figure 3

Relative permittivity-composition isotherms for hydrogen peroxide-water solutions, from Gross and Taylor (1950). Under the experimental conditions the solutions are supercooled

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Summary and Outlook

We have sketched an animated hypothetical picture, based on known chiral interactions of hydrogen peroxide and substituted peroxides with axial chirality, in which enantiospecific interactions of hydrogen peroxide with an almost-chiral RNA world preferentially select a D-RNA population that becomes progressively fitter in that environment, but have the opposite effect on the L population. Although these effects are small, as they must be, because large perturbations are more likely to wipe out life, or incipient life, than mediate and enhance it, their ultimate consequence can be the elimination of the L-population. In developing and deepening this picture, of course the devil will be in the detail. Detailed dynamical modelling currently underway by our group is based on the evolution of interacting, length-structured populations — i.e., population distributions, adapting a methodology that was developed by Diekmann et al. (1998) and furthered by Clother and Brindley (2000) for modelling physiologically structured populations, using temperature dependent rate constants and incorporating an enthalpy balance.

Our review of the physical properties of hydrogen peroxide suggests that its effects may be favourable in terms of mediating the RNA world.

The wide interest in the topic of this research may help explain the persistence in human cultures of vampire myths — when one reflects on it, or attempts to, as it were, in a sense we are all vampires, made of molecules that have no natural mirror images on this world, forever searching the universe for our mirror image alien counterparts . . .