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

How did Long Template Replication Originate?

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

Ganti’s Hypothesis: They originated in a Protocell. -Autocatalytic Formose Metabolism. -Autocatalytic Membrane System. -Autocatalytic Template Polymerisation.

Ganti’s computational model of template replication was unrealistic, assuming an initiation and apropagation reaction for template growth.

If nucleotide like molecules were produced by acellular metabolism, what would really happen to them?

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.

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.

Short Templates Can Replicate.

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

Our Findings.

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

Competition by successfully unzipping short replicators.

Premature detachment of incomplete copies from longer

strands

No unzipping of long double strands

Elongating side-reactions.

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.

Previous Models.

• An chemical kinetic model predicted replication at low temperature.

300K280K

High [monomer]

Low [monomer]

Methods

• Relax Assumptions about Reaction Mechanisms.

• Allow Representation of Many Possible Configurations.

• A Stochastic Model. • Non-Uniform Disjoint Cellular Automata.

Inspiration.

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 (rate*activity), 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.

What are Non-Uniform Cellular Automata?

state

neighborhood

In uniform cellular automata each cell obays the same transform-ation rules. In a NUCA, the transformation rules depend on the cell state.

What are Disjoint Cellular Automata?

Polymer 1

Polymer 2

Polymer 3

Polymer 4

Each polymer in Its own CA.

Association rulesdetermine inter-actions between CAs.

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.

VERY SLOW

Spontaneous Formation of P-bonds: we assume it is so slow that we do not model it.

A much more likely way for a p-bond to form is shown next……

QUITE SLOW

P-bonds can form between nucleotides, ‘on’ another p-bond opposite.

P-bonds also break. More easily on single strands than double strands.

Template Directed P-bond formation rate.

P-bond degradationrate.

P-bond formation and breakage are functions of temperature.

temperature

Rate

VERY FAST

VERY FAST

H-bonds form and break very quickly.

FAST

EVEN FASTER (10x - 100x)

H-bonds are cooperative, one h-bond helps others to form next to it.

10x more likely

Cooperativity works inside strands also. H-bonds are more likely toform next to other h-bonds.

Zipper H-bond formation can occur anywhere along a floppy end.

H-bonds are less likely to break if surrounded by other h-bonds.

Non-complementary h-bonds are 10x more likely to break than complementary ones.

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.

I model each separate polymer on a 2D grid topology, so…. Inner loops form transiently

Breathing occurs.

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.

e.g. 6 * 9 for the two polymers above.

Polymer A.

Polymer B.

Only associations that conform to the 2D grid topology are permitted.

Arbitrary configurations in the 2D grid topology are possible. E.g.

Many will be very unstable and only form transiently….

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.

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.

Control Experiments

Rare configurations will be under-represented due to the small numbers of polymers simulated.

Melting Temperature curves could be reproduced.

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.

Mechanism of Elongation can be Directly Observed.

Elongation Occurs only at Low Temperatures.

•

- Same conditions as

before.

- 121 hours.

- 320K.

What About Replication?

Long Sequence Replication Does Not Occur.

The Side-Reaction Problem is Ubiquitous

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

Design for a Replicase Ribozyme

Ligase (non-processive).

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.

Acknowledgements.

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