A Model of Non-Enzymatic Nucleic Acid Elongation and Replication.

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A Model of Non-Enzymatic Nucleic Acid Elongation
and Replication.

• Chrisantha Fernando,
• Eors Szathmary, Johan Elfo
• Center for Computational Neuroscience and
  Robotics, Dept. of Informatics, University of
  Sussex, Falmer, Brighton BN1 9RH, UK and
  Collegium Budapest (Institute for Advanced
  Study), Szentháromság u. 2, H-1014 Budapest,
  Hungary
• Dept of Plant Taxonomy and Ecology, Eötvös
  University, and Collegium Budapest (Institute for
  Advanced Study), Szentháromság u. 2, H-1014
  Budapest, Hungary
• oDept. of Cell Molecular Biology, Molecular
  Biology Programme, Biomedical Center, Box 596,
  Husarg. 3, SE-751 24 Uppsala, Sweden

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How did Long Template Replication Originate?

• The origin of template replication is a major
  unsolved problem in science.

• Gantis Hypothesis They originated in a
  Protocell.
• -Autocatalytic Formose Metabolism.
• Autocatalytic Membrane System.
• Autocatalytic Template Polymerisation.
• Gantis computational model of template
  replication
• was unrealistic, assuming an initiation and a
• propagation reaction for template growth.
• If nucleotide like molecules were produced by a
• cellular metabolism, what would really happen to
  them?

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The Replicase Ribozyme

• No Replicase Ribozyme has been found, designed,
  or artificially selected.
• How could a replicase ribozyme evolve?
• By natural selection acting on long RNA
  sequences.
• But replication is a prerequisite for evolution.
  
• Therefore another non-enzymatic means of long
  nucleic acid replication is needed.

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Long Templates Have Been Synthesized.

• Non-enzymatic synthesis of templates up to 55
  nucleotides has been achieved on mineral
  surfaces, but there is no replication, because
  templates do not recycle by unzipping.

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Short Templates Can Replicate.

• Short oligonucleotide analogues can
  self-replicate, but longer ones cannot because
  self-inhibition by strand association becomes
  prohibitive.

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Our Findings.

• We identify four main obstacles to the
  replication of longer strands.

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Competition by successfully unzipping short
replicators.
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Premature detachment of incomplete copies from
longer strands
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No unzipping of long double strands
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Elongating side-reactions.
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Elongation v. Replication.

• We show in silico that at low temperatures and
  high polymer concentrations, the first two
  obstacles are avoided, allowing unlimited
  elongation by association of staggered duplex
  oligomers. However, low temperatures magnify the
  last two obstacles.

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Previous Models.

• An chemical kinetic model predicted replication
  at low temperature.

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300K
280K
High monomer
Low monomer
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Methods

• Relax Assumptions about Reaction Mechanisms.
• Allow Representation of Many Possible
  Configurations.
• A Stochastic Model.
• Non-Uniform Disjoint Cellular Automata.

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Inspiration.
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What is a Stochastic Model?

• Represent an Integer number of molecules in a
  fixed volume reactor.
• For each possible reaction in the reactor,
  calculate a propensity (rateactivity), and
  generate a time according to the distribution
• ti -log(rand()/pi).
• Execute the reaction with the earliest ti.
• Update only the propensities that have been
  affected by the executed reaction.

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What are Non-Uniform Cellular Automata?
neighborhood
state
In uniform cellular automata each cell obays the
same transform- ation rules. In a NUCA, the
transformation rules depend on the cell state.
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What are Disjoint Cellular Automata?
Each polymer in Its own CA. Association
rules determine inter- actions between CAs.
Polymer 1
Polymer 3
Polymer 2
Polymer 4
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• Let the CA represent 2 types of activated
  monomers (nucleotides) with properties resembling
  nucleic acids.
• Able to make strong covalent bonds along the
  chain (P-bonds).
• Able to undergo base pairing (H-bonds) between
  opposite monomers.
• The H-bonds and P-bonds are the primitives of
  the stochastic model.

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Spontaneous Formation of P-bonds we assume it is
so slow that we do not model it.
VERY SLOW
A much more likely way for a p-bond to form is
shown next
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P-bonds can form between nucleotides, on
another p-bond opposite.
QUITE SLOW
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P-bonds also break. More easily on single
strands than double strands.
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P-bond formation and breakage are functions of
temperature.
Rate
Template Directed P-bond formation rate.
P-bond degradation rate.
temperature
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H-bonds form and break very quickly.
VERY FAST
VERY FAST
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H-bonds are cooperative, one h-bond helps others
to form next to it.
FAST
EVEN FASTER (10x - 100x)
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Cooperativity works inside strands also. H-bonds
are more likely to form next to other h-bonds.
10x more likely
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Zipper H-bond formation can occur anywhere along
a floppy end.
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H-bonds are less likely to break if surrounded by
other h-bonds.
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Non-complementary h-bonds are 10x more likely to
break than complementary ones.
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A simple 2o structure is assumed.

• Nucleotides exist on a 2D grid, with p-bonds
  forming horizontally, and h-bonds forming
  vertically.
• Hairpins cannot form in this topology.

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Inner loops form transiently
I model each separate polymer on a 2D grid
topology, so.
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Breathing occurs.
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The chance of the first h-bond being formed
between two polymers depends on the product of
available h-bond sites on those two polymers.
Polymer B.
Polymer A.
e.g. 6 9 for the two polymers above.
Only associations that conform to the 2D grid
topology are permitted.
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Arbitrary configurations in the 2D grid topology
are possible. E.g.
Many will be very unstable and only form
transiently.
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Others will be more stable We do not predefine
the expected configurations in the effectively
infinite space of all possible configurations.
They arise due to the underlying intra- and
inter- polymer dynamics I have described.
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Two Time-Scale Dynamics

• P-bonds form and break much slower than H-bonds.
  
• Run H-bond dynamics to equilibrium.
• Sample microstates at equilibrium.
• Calculate p-bond formation and breakage
  propensities for each microstate, and execute a
  p-bond event.

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Control Experiments
Rare configurations will be under-represented
due to the small numbers of polymers simulated.
Melting Temperature curves could be
reproduced.
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Results
Initialized with 50 ds 6-mers (0.0016M), and 20
monomers (10 A, and 10 B) (0.0006M). 280K, 7.8
years. Longest polymer length 103.
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Mechanism of Elongation can be Directly Observed.
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Elongation Occurs only at Low Temperatures.

• Same conditions as
• before.
• - 121 hours.
• - 320K.

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What About Replication?
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Long Sequence Replication Does Not Occur.
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The Side-Reaction Problem is Ubiquitous

• Side-Reactions Interfere with replication, both
  in template replication and in the evolution of
  metabolism!

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Design for a Replicase Ribozyme
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Ligase (non-processive).
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QB Replicase.

• It worked very nicely.
• Can replicate unlimited lengths of strand.
• Processivity crucial.
• But too complex!
• The possibility of an unintuitive emergent
  replicase function.

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Acknowledgements.

• Eors Szathmary
• Guenter Von Kiedrowski
• Karin Achilles
• Mons Ehrenburg
• Jarle Breivik
• Simon McGregor
• Andy Balaam
• Cost D27 Program in Prebiotic Chemistry.