Gard model

The composition vector of an assembly is written as: ${\displaystyle v=n_{1}\cdots n_{N_{G}}}$. Where ${\displaystyle n_{1}\cdots n_{N_{G}}}$ are the molecular counts of lipid type i within the assembly, and NG is how many different lipid types exist (repertoire size).

The change in the count of molecule type i is described by:

${\displaystyle {\frac {dn_{i}}{dt}}=(k_{f}\rho _{i}N-k_{b}n_{i})\left(1+\sum _{j=1}^{N_{G}}\beta _{ij}{\frac {n_{j}}{N}}\right)}$

${\displaystyle k_{f}}$ and ${\displaystyle k_{b}}$ are the basel forward (joining) and backward (leaving) rate constants, β_ij is a non-negative rate enhancement exerted by molecule type j within the assembly on type i from the environment, and ρ is the environmental concentration of each molecule type. β is viewed as a directed, weighted, complex network.

The assembly current size is ${\displaystyle N=\sum _{i=1}^{N_{G}}n_{i}}$. The system is kept away from equilibrium by imposing a fission action once the assembly reaches a maximal size, Nmax, usually in the order of NG. This splitting action produces two progeny of same size, and one of which is grown again.

The model is subjected to a Monte Carlo algorithm based simulations, using Gillespie algorithm.

In 2010, Eors Szathmary and collaborators have chosen GARD as an archetypal metabolism-first realization.[3] They have introduced selection coefficient into the model, which increase or decrease the growth rate of assemblies, depending on how similar or dis-similar they are to a given target. They found that the ranking of the assemblies are un-affected by the selection pressure, and concluded that GARD does not exhibit Darwinian evolution.

In 2012 it was shown that this criticism is erroneous and was refuted by Doron Lancet and Omer Markovitch.[4] Two major drawbacks of the 2010 paper were: (1) they have focused on a general assembly and not on a composome or compotype (faithfully replicating and quasispecies, respectively); (2) they have performed only a single, random, simulation to test the selectability.

The quasispecies model describes a population of replicators that replicate with relatively high mutations. Due to mutations and back mutations the population eventually centres around a master-replicator (master sequence). GARD's populations were shown to form a quasispecies around a master-compotype and to exhibit an error catastrophe, similarly to classical quasispecies such as RNA viruses.[5]

• Abiogenesis
• Protocell

• GARD10 MATLAB code (see Markovitch and Lancet, 2012): https://github.com/ModelingOriginsofLife/GARD
• Doron Lancet homepage at Weizmann Institute of Science, who is the inventor of GARD.
• Origin of life (OOL Archived 2007-07-10 at the Wayback Machine) at the Weizmann Institute.