Chemical Convection Cells or The Origin of Recycling

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Chemical Convection Cellsor The Origin of
Recycling

• Chrisantha Fernando
• University of Birmingham, UK
• Autonomy Workshop AlifeX, Bloomington Indiana,
  June 2006

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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.

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Kauffman Side-steps Side-Reactions
If growth of the adjacent possible reactions is
prop- ortional to the n, then the system is
spreading.
Kauffmans Universe
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)
Our Universe
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Kauffman Ignores Precursor Depletion
If there is depletion then the precursors of the
set must be re-cycled! In Kauffmans universe
there is constant excess of precursors. In
our universe, we need to explain why they
dont run out.
Kauffmans Universe
Our Universe
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Re-formulating the Problem
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Is this is analogous to the pre-Benard cell state
h
h
Funneling
p
p
- 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.
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How to get a chemical Benard Instability?
h
h
Motion of high energy matter to the sink does not
undergo a combinatorial explosion, but passes
through a low dimensional channel.
Recycling of the low energy matter to the p
absorbing state is increased.
p
What types of generative chemistry result in the
production of these types of re-configuration?
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The Abiosphere
h
X
p
W
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Rare chemical events enlarge the chemical network
h
X
Y
p
W
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Type Ia Spontaneous Reactions
h
Rearrangement
h
X
Y
p
W
A reaction is favorable when the Gibbs Free
Energy change (?G) of that reaction is negative.
?G ?H - T?S, ?H being the change in enthalpy,
and ?S is the change in entropy. So for the
reaction X ---gt Y, ?G Gx-Gy.Ive lumped the ?H
- T?S terms into the number h. Ive assumed an
isothermic reactor. e.g. 1. Photosynthesis.
6CO2 6H2O --gt glucose 6O2 . ?G 686
kcal/m 2. ATP H2O --gt ADP phophate, ?G
-7.3 kcal/m
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Type Ib Spontaneous Reactions
h
h
Cleavage
X
Y
Z
p
W
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Type Ic Spontaneous Reactions
h
h
Ligation
X
Z
p
W
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Type IIa Energy Absorbing Reactions
h
Rearrangement
X
p
Y
p
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Type IIb Energy Absorbing Reactions
h
Cleavage
X
p
Y
Z
p
W
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Type IIc Energy Absorbing Reactions
h
Ligation
X
p
Z
p
W
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Particle Structure

• Chemical species are strings of letters a,
  b, c
• Total string number (mass) is conserved.
• 1. aababa ----gt aaaabb (A possible
  rearrangement).
• 2. aababa ----gt aaaa bb (A possible
  cleavage).
• 3. aababa bb ----gt aabbabba (A possible
  ligation).

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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 ---gt B 1 Ea Eb
• 1b A p ---gt B C 1 Ea Eb Ec
• 1c A B p ---gt C Ea Eb 1 Ec
• 2a A ---gt B h Ea Eb Eh
• 2b A ---gt B C h Ea Eb Ec Eh
• 2c A B ---gt 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.

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Compare Three Simple Generative Regimes

• Random choice of reactants and products (i.e.
  independent of chemical dynamics!).
• Choose reactants in proportion to Free Energy x
  Concentration
• 2 Force at least one of the products to already
  be in existence (so reducing spreading).

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Here is an example of 3.

First heat producing reaction
Starting Molecule
First light absorbing reaction
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New reaction aa aaa p ---gt a aaaa
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New reaction aaaa aaaa p ---gt aaaaa aaa
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New reaction aaaaa lt---gtaaaa a h
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New reaction aaaaa lt---gtaaa aa h
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New reaction aaaa lt---gtaaa a h
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New reaction aaa aaaa lt---gtaaaaaa a h
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New reaction aaaaaa aaaaaa p -gt a
aaaaaaaaaaa
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Does re-cycling arise and tend to increase?

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

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Total Light Absorption Rate.
3. 2 Force at least one of the products to
already be in existence.

• Random choice of reactants
• and products.

0.0001
0.000025
Total Light Absorption Rate.
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?

0.0000005
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The random generation of cycles results in a
chemical system with 2 orders of magnitude more
internal energy than the probabilistic regimes!
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How does the structure of the networks depend on
the generative regime?
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No clear relationship between degree distribution
and re-cycling capacity.
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No clear relationship between path length and
re-cycling.
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No clear relationship between re-cycling
capacity and clustering coefficient.
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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?