A Model of Chemical Evolution by Artificial Selection for Energy Flux Maximization Chrisantha Fernando & Jon Rowe School of Computer Science University of Birmingham UK Dublin, 2006 Chrisantha Fernando & Jon Rowe School of Computer Science University of Birmingham UK Dublin, 2006

Aim  To help chemists create dissipative structures capable of the ‘recursive generation of functional constraints’ (RGFC).  e.g. life.  To help chemists create dissipative structures capable of the ‘recursive generation of functional constraints’ (RGFC).  e.g. life.

Examples of Dissipative Structures not capable of RGFC Gravity Convection Arguably, clouds have not improved in 4 billion years.

What is the Minimal Dissipative Structure capable of RGFC?  Circulation must produce novel products capable of positive feedback on the circulation.  But lets be realistic.  Circulation must produce novel products capable of positive feedback on the circulation.  But lets be realistic. X + An imaginary adaptive novelty in Cloudoid

Most random novel products are harmful  X is likely to be either neutral or harmful.  The solution is to have many clouds to prevent Muller’s Ratchet.  X is likely to be either neutral or harmful.  The solution is to have many clouds to prevent Muller’s Ratchet. X 0/- An imaginary harmful or neutral novelty

X 0/- X X X X + X X X X X X X X X X X

Low Rate of Novel Product Formation is Preferable.  To prevent harmful products ‘drowning out’ the good ones.  To prevent harmful products ‘drowning out’ the good ones. X 0/- Y +

But even then,the rare adaptive novelty is lost by dilution. X + X/2 + + H2OH2O

To prevent this, X must at least double with the doubling period of the cloud X + X + X + H2OH2O X

The Cloud Selection Machine  Natural selection can apply if  The entities self-replicate.  Undergo heritable adaptive novelties.  Natural selection can apply if  The entities self-replicate.  Undergo heritable adaptive novelties.

Puddle Puddle = non-dissipative cloud, e=0, f=0 Less dissipative cloud f 2 <f 1 More dissipative cloud f 2 >f 1 E 1 m 1 =f 1 E 2 m 2 =f 2 More dissipative cloud f 2 >f 1. But proliferated, not self-replicated. Generation 1

Generation 2 E 2 m 2 =f 2 Selfreplicating Type. E 2 m 2 =f 2 : Proliferating Type. Puddle The proliferating type only has one chance for an adaptive novelty. The self-replicating type has two extra chances per generation of an adaptive novelty.

Cloudoids vs. Clouds  Cloudoids exhibit unlimited production of autocatalytic products, X.  Cloudoids self-replicate, clouds generally don’t. They proliferate.  So how do we make a real cloudoid?  With a richer chemistry than that of clouds, and a different energy source. No living system known feeds on gravity like clouds do.  Cloudoids exhibit unlimited production of autocatalytic products, X.  Cloudoids self-replicate, clouds generally don’t. They proliferate.  So how do we make a real cloudoid?  With a richer chemistry than that of clouds, and a different energy source. No living system known feeds on gravity like clouds do.

Multiple Sources for a ‘Rich’ Chemistry  A.I. Oparin & J.B.S. Haldane (1924,1929). UV light energy  G. Wachtershauser. FeS/H 2 S reducing power produces COO -, -S -, -COS -.  S. Miller. Electrical discharges.  C. de Duve. Thioester metabolism on surfaces.  H. Morowitz. Reverse Citric acid cycle on mineral surfaces.  Decker, Ganti. Formose cycle feeding on Formaldehyde from CO and H 2 O + light.  Chyba and Astrobiology. Organics from space.  A.I. Oparin & J.B.S. Haldane (1924,1929). UV light energy  G. Wachtershauser. FeS/H 2 S reducing power produces COO -, -S -, -COS -.  S. Miller. Electrical discharges.  C. de Duve. Thioester metabolism on surfaces.  H. Morowitz. Reverse Citric acid cycle on mineral surfaces.  Decker, Ganti. Formose cycle feeding on Formaldehyde from CO and H 2 O + light.  Chyba and Astrobiology. Organics from space.

Given this chemical detail, how can a model help a chemist?  Identify capacity for RGFC in generative chemistries that are at least subject to conservation of mass and energy.  The chemist can look at what the imaginary chemist does with such imaginary chemistries to get RGFC, and wonder whether they can do the same with their pet chemistry.  Identify capacity for RGFC in generative chemistries that are at least subject to conservation of mass and energy.  The chemist can look at what the imaginary chemist does with such imaginary chemistries to get RGFC, and wonder whether they can do the same with their pet chemistry.

Our Imaginary Chemistry  Consists of bimolecular rearrangement reactions of binary atoms, e.g.  abbb + ba abb + abb  Each molecule has free energy of formation, G.  Two types of reaction.  Reversible exogonic reactions (heat producing)  Irreversible endogonic reaction (‘light absorbing)  Consists of bimolecular rearrangement reactions of binary atoms, e.g.  abbb + ba abb + abb  Each molecule has free energy of formation, G.  Two types of reaction.  Reversible exogonic reactions (heat producing)  Irreversible endogonic reaction (‘light absorbing)

k f = e -dG/RT k b = 0.01, dG = (G products - G reactants ) R = gas constant, T = 300K

Artificial Selection abbb ba, ab abbb

How does novelty arise?  Control (Ideal) Experiment  Allow the random production and deletion of novel high flux reactions.  Full Experiment  Allow N novel low flux reactions per generation.  Then determine the high flux reactions in which novel products take part, by assuming they react at random with proportion P of any existing species.  This results in a reaction avalanche.  Control (Ideal) Experiment  Allow the random production and deletion of novel high flux reactions.  Full Experiment  Allow N novel low flux reactions per generation.  Then determine the high flux reactions in which novel products take part, by assuming they react at random with proportion P of any existing species.  This results in a reaction avalanche.

babb + abbb babb babb + ba ---> abb + abb babb + ab ---> bbb + aa bbb + babb ---> perhaps more novel products. Etc… aa + ba ---> perhaps more novel products. The Reaction Avalanche

Bolus of abbb used. Bolus of abbb not used

What does the group II network do?  Fitness is largely unaffected if the network is initialized with 100mM abbb plus any one of the following species at 0.1mM; ba, ab, abb, babb, babbb, bbbbbba. However, if the network is initialized with 100mM abbb alone, or with 100mM abbb + 0.1mM bbab, bbabab, bbbba, bab, bbabb, or bbbaabab, etc… then fitness = 0.  I.e. the network reacts abbb (food) with inherited high energy molecules (self) to produce abb.  Fitness is largely unaffected if the network is initialized with 100mM abbb plus any one of the following species at 0.1mM; ba, ab, abb, babb, babbb, bbbbbba. However, if the network is initialized with 100mM abbb alone, or with 100mM abbb + 0.1mM bbab, bbabab, bbbba, bab, bbabb, or bbbaabab, etc… then fitness = 0.  I.e. the network reacts abbb (food) with inherited high energy molecules (self) to produce abb.

Autocatalytic Behaviour of Group II networks

The characteristic delay phase of autocatalysis.

Conclusion from Control Experiment  Where there is no explicit engram that preserves novel reactions, with selection for high energy flux, and dilution pressure, the light absorbing species, the system evolves to autocatalytically produce abb. Food abbb utilizes high energy inherited matter to produce abb rapidly.  We have shown this selection regime is sufficient to account for the origin of growth autocatalysis.  Where there is no explicit engram that preserves novel reactions, with selection for high energy flux, and dilution pressure, the light absorbing species, the system evolves to autocatalytically produce abb. Food abbb utilizes high energy inherited matter to produce abb rapidly.  We have shown this selection regime is sufficient to account for the origin of growth autocatalysis.

The Full Experiment  Now we run the same experiment, but where novel low flux reactions produce products that may or may not be autocatalytic and cross-catalytic.

abbb

A Problem with the generative algorithm.

All novel high flux reactions must be irreversible to prevent this unrealistic solution.

More cheating!  X + ba  X + ab. Selfish parental adaptations.  Rare reactions directly provided a slight advantage to the parent.  Therefore, rare reaction rate set to zero, and initial concentration of product set to instead of  When this was done, none of the ‘cloud type’ adaptations were produced!!! WHY????  X + ba  X + ab. Selfish parental adaptations.  Rare reactions directly provided a slight advantage to the parent.  Therefore, rare reaction rate set to zero, and initial concentration of product set to instead of  When this was done, none of the ‘cloud type’ adaptations were produced!!! WHY????

The difficulty with evolving a ‘cloud type’ adaptation. 1.All three reactions must occur at once. 2.NOT ONLY THIS!!!! The kinetics must be such that k 4 is high in comparison to k 5. Infact [abbb] > k 4 /k 5, k 4 /k 5 is the ‘food threshold’ of the autocatalytic particle [babb] above which [abbb] must be for babb to not decay to zero. 3.To allow any chance of this happening, we have to increase the rates of novel high flux reactions. abbb + ba --> babb + ba

k4 = 1, k5 = 1k4 = 2, k5 = 1 k4 = 2.5, k5 = 1 k4 = 3, k5 = 1

Networks Evolved with Stringent Parameters  Zero rare flux.  Very low initial product concentration ( M, still unrealistically high)  High flux (1000x to 5000x greater than before) and (almost) irreversible novel reactions, (backrate = sec -1 M -1 )  Zero rare flux.  Very low initial product concentration ( M, still unrealistically high)  High flux (1000x to 5000x greater than before) and (almost) irreversible novel reactions, (backrate = sec -1 M -1 )

[abbb] Fitness = 1500 [abb] Network 12 abbb only Cheating again!

With these constraints, ‘cloud type’ adaptations not yet evolved. Is this because three different serendipitous types of reaction must simultaneously arise? ‘Cheat’ solutions were much more likely. As network size grows, P = 0.01 produces too much interference, i.e. the mean avalanche sizes suitable for a small network are not suitable for larger ones. Perhaps if MOST interactions were weak, this would be solved. We have drawn the kinetics from a uniform distribution, not a log-normal distribution for example.

Lessons for the Chemist?

 For RGFC, the generative chemistry must be capable of unlimited production of engram autocatalysts with achievable food threshold, and capable of suitable activity at the higher level.  Dilution and selection for high energy flux should result in the entire system exhibiting growth autocatalysis because this results in efficient abb production.  Very large population sizes will be required due to the requirement for 3 novel reactions to occur at once, thus microfluidics will be required.  Alternatively, one should allow selection for pre- adaptations, e.g. generic autocatalysts that might later be able to obtain the right flask level properties, e.g. RNA. This requires a different fitness function.  For RGFC, the generative chemistry must be capable of unlimited production of engram autocatalysts with achievable food threshold, and capable of suitable activity at the higher level.  Dilution and selection for high energy flux should result in the entire system exhibiting growth autocatalysis because this results in efficient abb production.  Very large population sizes will be required due to the requirement for 3 novel reactions to occur at once, thus microfluidics will be required.  Alternatively, one should allow selection for pre- adaptations, e.g. generic autocatalysts that might later be able to obtain the right flask level properties, e.g. RNA. This requires a different fitness function.

Thanks to…..  Jon Rowe  Kepa and Xabier (San Sabastian, Autonomy Workshop, Alife X)  Eors Szathmary  Hywel Williams  Alex Penn  Tibor Ganti, Guenter Wachtershauser, Robert Hazen.  Jon Rowe  Kepa and Xabier (San Sabastian, Autonomy Workshop, Alife X)  Eors Szathmary  Hywel Williams  Alex Penn  Tibor Ganti, Guenter Wachtershauser, Robert Hazen.