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Table 1 Parameters used in the Monte Carlo simulations

From: Circularity and self-cleavage as a strategy for the emergence of a chromosome in the RNA-based protocell

Probabilities

Descriptions

Values *

P AD

Amphiphile decaying into its precursor (out of membrane)

5 × 10-4

P ADM

Amphiphile decaying into its precursor within membrane

5 × 10-5

P AF

Amphiphile forming from its precursor (not catalyzed)

5 × 10-4

P AFR

Amphiphile forming from its precursor (catalyzed by Asr)

0.9

P AJM

Amphiphile joining membrane

0.9

P ALM

Amphiphile leaving membrane

5 × 10-5

P APP

Amphiphile precursor permeating membrane

0.05

P AT

RNA attracting nucleotides/oligomers by base-pairing

0.2

P BB

Phosphodiester bond breaking in an RNA chain

2 × 10-6

P CB

Protocell breaking

1 × 10-5

P CD

Protocell dividing

0.02

P CF

Protocell fusing

5 × 10-4

P CRTT

A circular RNA turning to a template

0.9

P EL

End-to-end ligation of an RNA chain (cyclization)

1 × 10-7

P FLR

Ligating with false base-pairing on template (by Rep)

0.01

P FP

False base-pairing in RNA attracting nucleotides/oligomers

0.01

P LRTT

A linear RNA turning to a template (i.e., unfolding)

0.01

P MC

Movement of a protocell

0.05

P MF

Membrane forming

0.1

P MV

Movement of a nucleotide, amphiphile or their precursors

0.5

P ND

Nucleotide decaying into its precursor

5 × 10-4

P NDE

Nucleotide decaying into its precursor at RNA’s chain end

2 × 10-5

P NF

Nucleotide forming from its precursor (not catalyzed)

5 × 10-4

P NFR

Nucleotide forming from its precursor (catalyzed by Nsr)

0.9

P NPD

Nucleotide precursor decaying into its precursor

5 × 10-4

P NPF

Nucleotide precursor forming from its precursor (not catalyzed)

5 × 10-4

P NPFR

Nucleotide precursor forming from its precursor (catalyzed by Npsr)

0.9

P NPP

Nucleotide precursor permeating membrane

0.01

P NPPP

Nucleotide precursor’s precursor permeating membrane

0.2

P RB

Rep binding onto an RNA template

0.9

P RD

Rep dropping from an RNA template

0.9

P RL

Random ligation of nucleotides and RNA

1 × 10-7

P SP

Separation of a base pair

0.5

P TL

Template-directed ligation (not catalyzed)

5 × 10-4

P TLR

Template-directed ligation (catalyzed by Rep)

0.9

Others

Descriptions

Values *

F DE

Factor for the effect of Donnan’s equilibrium [28]

5

F DO

Factor for the degradation/decay of molecules out of protocells

20

F IB

Factor for intermediate RNA breaking (at sites between genes)

100

F OP

Factor for the effect of osmotic pressure [27]

5

L AM

Lower limit of amphiphiles to form protocell membrane

600

N

The system surface is defined as an N × N grid.

40

T APB

Total amphiphile precursors introduced in the beginning

6 × 104

T NPPB

Total nucleotide precursors’ precursors introduced in the beginning

8 × 104

  1. * This set of parameter values is for the case shown in Figure 2, and also represents the common parameter list that was used for the parameter analysis in Figure 4 and in the Additional file 1: Figures S2-S5.