Synchronization of replicator and aggregate growth

The primitive proto-organism that is envisioned in the PACE project consist of three parts: a lipid aggregate, information carrying proto-gene molecules and metabolically active chemical substrates. Central to the function of the proto-cell is the ability to grow and divide, i.e. replicate, through self-regulating chemical processes. It is however not clear how this should be achieved since no coordinating central control is present in the system. It could easily be the case that for example the growth and replication of the aggregates happen on a faster time scale than the replication of the genome, resulting in the production of aggregated with no genomic information connected to them. In more advanced life forms this, and many other things, are avoided by carefully regulated replication cycles. In the proto-cell we have shown that the same regulation can be achieved spontaneously by using a simple coupling between the gene replication and the container growth process.


The information carrying proto-genes replicate though complementary base pairing. Potentially this is a problem since it is well known that chemical processes determined by templating replication result in parabolic growth. This result follows from the equilibrium condition:

 clip_image001

 (1)

 

 

where Ts denotes the concentration of single stranded proto-genes and Td  denoted concentration of double stranded molecules. The growth of the population of proto-genes is then parabolic (to first order):

clip_image002

 

(2)

 

Since the population dynamics of the aggregate is driven by growth and spitting, it is typically expected to be exponential. The problem is clear: can we expect the aggregate and the genes to grow and divide synchronously?


The central idea is that the proto-genes should act differently in the single and the double stranded state, and in addition that the concentrations considered in the definition of Ts and Td are local, rather than global, concentrations. As a result there is a natural feedback mechanism where the aggregate growth shifts the relative concentration of single stranded and double stranded molecules according to Eq. 1 (interpreted in terms of local concentrations in each aggregate). The different action in the single and double stranded state is as follows. It is obvious that the replication rate of the proto-genes is propotional to the number of single stranded molecules, since it is in this state that the molecule is ready to be copied. In the double stranded state the proto-genes do not replicate themselves, however as the chemical setup in the minimal protot-cell is envisioned the double stranded information molecules promote the aggregate to grow though catalysis of lipid component. As a result, the overall system self-regulate the growth and the resulting population dynamics is a synchronized exponential growth (limited by the available precursor resources).


Reference:

T. Rocheleau, S. Rasmussen, P. E. Nielsen, M. N. Jacobi and H. Ziock (2007). Emergence of protocellular growth laws. Phil. Trans. Roy. Soc. Lond. ser. B 362, 1841-1845.