Chemical Convection Cells or The Origin of Recycling

Chemical Convection Cellsor The Origin of Recycling

Chrisantha Fernando

University of Birmingham, UK

Autonomy Workshop AlifeX, Bloomington Indiana, June 2006

Question

• What features of a chemistry and its reactor can allow ‘chemical evolution’, i.e. the origin of entities with ‘basic autonomy’, ultimately capable of the synthesis of complex template replicators, and hence of microevolution?

• What in practice must a chemist do to avoid the synthesis of tar (a combinatorial explosion of stable polymers), and obtain a chemical system capable of the ‘recursive generation of functional constraints’?

• Here I outline the core physical constraints that should be acknowledged before a practical answer to this question can arise, i.e. conservation of mass and energy in a closed (not isolated) reactor. We cannot assume the continued abundance of precursors nor a magical barrier to side-reactions as Kauffman has done. This is our explanandum.

Kauffman Side-steps Side-Reactions

Calculations of probabilities about suchsystems always assume that a protein may or may notcatalyse a given legitimate reaction in the system but thatit would not catalyse harmful side reactions. This isobviously an error. Hence the paradox of specificitystrikes again -- the feasibility of autocatalytic attractorsets seems to require a large number of component types(high n), whereas the plague of side reactions calls forsmall systems (low n). (Eors Szathmary, 2000)

If growth of the ‘adjacentpossible’ reactions is prop-ortional to the n, then thesystem is ‘spreading’.

Kauffman’sUniverse

OurUniverse

Kauffman Ignores Precursor Depletion

If there is depletion then…the precursors of the setmust be re-cycled!

In Kauffman’s universe there is constant excess of precursors.

In our universe, we need to explain why they don’trun out.

Kauffman’sUniverse

OurUniverse

Re-formulating the Problem

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

p

h

- With diffusion alone, there is a combinatorial explosion ofpossible paths by which energy can move from p to h, but at least the since of the surface stays constant!

- In a standard chemical system we have the following (not to scale)… - Re-cycling to the heat absorbing surface becomes more unlikely as thechemical heat sink increases by combinatorial explosion.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

p

h

Is this is analogous to the pre-Benard cell state

Funneling

How to get a chemical Benard Instability?

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Recycling of the low energy matter tothe p absorbing state is increased. p

Motion of high energy matterto the sink does not undergoa combinatorial explosion, butpasses through a lowdimensional channel.

h h

What types of generative chemistry result in the production of these types of re-configuration?

The Abiosphere

X

W

p

h

Rare chemical events enlarge the chemical network

X

W

p

h

Y

Type Ia: Spontaneous Reactions

X

W

p

h

Y

Rearrangement h

A reaction is favorable when the Gibbs Free Energy change (ΔG) of that reaction is negative. ΔG = ΔH − TΔS, ΔH being the change in enthalpy, and ΔS is the change in entropy. So for the reaction X ---> Y, ΔG = Gx-Gy.I’ve lumped the ΔH − TΔS terms into the number “h”. I’ve assumed an isothermic reactor.

e.g. 1. Photosynthesis. 6CO2 + 6H2O --> glucose + 6O2 . ΔG = +686 kcal/m

2. ATP + H2O --> ADP + phophate, ΔG = -7.3 kcal/m

X

W

p

h

Y

Cleavage

Z

h

Type Ib: Spontaneous Reactions

X

W

p

hLigation

h

Z

Type Ic: Spontaneous Reactions

X

p

h

Y

Rearrangement

Type IIa: Energy Absorbing Reactions

p

X

W

p

h

Y

Cleavage

Z

p

Type IIb: Energy Absorbing Reactions

X

W

p

hLigation

Z

p

Type IIc: Energy Absorbing Reactions

Particle Structure

• Chemical species are strings of letters: ‘a’, ‘b’, ‘c’…

• Total string number (mass) is conserved.

1. aababa ----> aaaabb (A possible rearrangement).

2. aababa ----> aaaa + bb (A possible cleavage).

3. aababa + bb ----> aabbabba (A possible ligation).

MethodInitialization

• Start with one molecule type ‘a’, at concentration 100, with uniform random assignment of ‘free energy from range 0-1. • Randomly choose a molecule to undergo a light absorbing reaction (obviously at first this will just be ‘a’). All p has energy 1 and is

present at concentration 1. • Randomly choose (1,2) molecules to undergo a heat producing reaction. This may or may not result in a re-cycling system. • When generating each reaction I ensure that it is energy conserving as follows. • 1a: A + p ---> B {1 + Ea = Eb} • 1b: A + p ---> B + C {1 + Ea = Eb + Ec}• 1c: A + B + p ---> C {Ea + Eb + 1 = Ec}• 2a: A ---> B + h {Ea = Eb + Eh} • 2b: A ---> B + C + h {Ea = Eb + Ec + Eh}• 2c: A + B ---> C + h {Ea + Eb = Ec + Eh}

If the products already exist, I.e. if they have already been assigned a free energy in a previous reaction generation step, then it may not be possible to satisfy the equalities, and this reaction is rejected.

The free energies affect the rates of the reactions as follows. All light absorbing reactions are irreversible and have rate = 1. All heat producing reactions are reversible and have backward rate = 1, and….

forward rate = eh/RT

Iteration• The dynamics of the chemical network are simulated by numerical integration of standard chemical kinetics equations using the

above rates. An upper limit to forward rate is set at 100. The Eular integration time-step is 0.0001. Between each new reaction the system is simulated for 100000 time-steps.

Compare Three Simple Generative Regimes

1. Random choice of reactants and products (i.e. independent of chemical dynamics!).

2. Choose reactants in proportion to Free Energy x Concentration

3. 2 + Force at least one of the products to already be in existence (so reducing ‘spreading’).

Here is an example of 3.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Starting Molecule

First light absorbing reaction

First heat producing reaction

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

New reaction: aa + aaa + p ---> a + aaaa

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

New reaction: aaaa + aaaa + p ---> aaaaa + aaa

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

New reaction: aaaaa <--->aaaa + a + h

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

New reaction: aaaaa <--->aaa + aa + h

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

New reaction: aaaa <--->aaa + a + h

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

New reaction: aaa + aaaa <--->aaaaaa + a + h

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

New reaction: aaaaaa + aaaaaa + p -> a + aaaaaaaaaaa

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Does re-cycling arise and tend to increase?

I define re-cycling as the steady state level of light absorption.

0.0001

Total Light Absorption Rate.

0.000025

Total Light Absorption Rate.

0.0000005

3. 2 + Force at least one of the products

to already be in existence. 1. Random choice of reactants

and products.

2. Choose reactants in proportion

to Free Energy x Concentration

Re-cycling is highest in the completelyrandom regime!

But…

Statistical analysis is required. Q1. Is this always the case?

Q2. What is the proportion of light absorbing reactions produced by the different regimes?

The random generation of cycles results in a chemical system with 2 orders of magnitude more internal energy than the probabilisticregimes!

How does the structure of the networks depend on the

generative regime?

No clear relationship betweendegree distribution and re-cycling capacity.

7

No clear relationship betweenpath length and re-cycling.

No clear relationship between re-cycling capacity and clustering coefficient.

Conclusions

• I was surprised at first that the biased generative regime resulted in less re-cycling. However, in retrospect this is obviously because the few short recycling loops (likely to be of high energy) experience the most side-reactions due to this bias. This makes the funneling even worse.

• If it is the case that high energy particles are more likely to undergo further reactions, i.e. their features contribute most to the exploration of the chemical space, then it is only if such an exploration can somehow achieve greater re-cycling potential that the system can circumvent the ‘Funneling catastrophe’.

• How can this be achieved? – 1. The probability of reaction must be a function not only of the energy of reactants but

of reactant STRUCTURE. In particular, I predict that if high energy particles have the greatest capacity for re-configuration to obtain reaction specificity, then even if this re-configuration is random, that the system will tend towards increased steady state heat dissipation. Effectively, this may produce a Benard type instability by high energy particles doing random chemical pruning of their reactions.

– 2. Chemicals also have physical properties that can mediate physical specificity, e.g. by semi-permeability and diffusion limitation in a 2D or 3D space.

How to model chemical particle structure?