Chemical Convection Cells or 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 such systems always assume that a protein may or may not catalyse a given legitimate reaction in the system but that it would not catalyse harmful side reactions. This is obviously an error. Hence the paradox of specificity strikes again -- the feasibility of autocatalytic attractor sets seems to require a large number of component types (high n), whereas the plague of side reactions calls for small systems (low n). (Eors Szathmary, 2000) If growth of the ‘adjacent possible’ reactions is prop- ortional to the n, then the system is ‘spreading’. Kauffman’s Universe Our Universe

Kauffman Ignores Precursor Depletion If there is depletion then… the precursors of the set must be re-cycled! In Kauffman’s universe there is constant excess of precursors. In our universe, we need to explain why they don’t run out. Kauffman’s Universe Our Universe

Re-formulating the Problem

p h - With diffusion alone, there is a combinatorial explosion of possible 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 the chemical heat sink increases by combinatorial explosion. p h Is this is analogous to the pre-Benard cell state Funneling

How to get a chemical Benard Instability? Recycling of the low energy matter to the p absorbing state is increased. p Motion of high energy matter to the sink does not undergo a combinatorial explosion, but passes through a low dimensional 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 = G x -G y. I’ve lumped the ΔH − TΔS terms into the number “h”. I’ve assumed an isothermic reactor. e.g. 1. Photosynthesis. 6CO 2 + 6H 2 O --> glucose + 6O 2. ΔG = +686 kcal/m 2. ATP + H 2 O --> ADP + phophate, ΔG = -7.3 kcal/m

X W p h Y Cleavage Z h Type Ib: Spontaneous Reactions

X W p h Ligation 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 h Ligation 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).

Method Initialization 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 + E a = E b } 1b: A + p ---> B + C {1 + E a = E b + E c } 1c: A + B + p ---> C{E a + E b + 1 = E c } 2a: A ---> B + h {E a = E b + E h } 2b: A ---> B + C + h {E a = E b + E c + E h } 2c: A + B ---> C + h{E a + E b = E c + E h } 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 = e h/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 Between each new reaction the system is simulated for 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 Force at least one of the products to already be in existence (so reducing ‘spreading’).

Here is an example of 3. Starting Molecule First light absorbing reaction First heat producing reaction

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

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

New reaction: aaaaa aaaa + a + h

New reaction: aaaaa aaa + aa + h

New reaction: aaaa aaa + a + h

New reaction: aaa + aaaa aaaaaa + a + h

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

Does re-cycling arise and tend to increase? I define re-cycling as the steady state level of light absorption.

Total Light Absorption Rate Total Light Absorption Rate 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 completely random 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 probabilistic regimes!

How does the structure of the networks depend on the generative regime?

No clear relationship between degree distribution and re-cycling capacity.

7 No clear relationship between path 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?