Growth Morphologies

red ball Competing variants would generically expand at different rates.

yellow ball The bulging circular arc is a common morphology for growth of a fitter mutant:

"Selective sweeps in growing microbial colonies,"

K.S. Korolev, M.J.I. Muller, N, Karahan, A.W. Murray, O. Halatschek, D.R. Nelson, Phys. Biol 9, 026008 (2012)

red ball Possible morphologies can be explored by coupling expansion profile (KPZ) and invasion (FKPP) equations (neglecting noise):

              

yellow ball Uniform (isotropic) growth constrains parameters of the above (gradient expnasion) equations to

            

A more general class of equations, also including anisotropy, were proposed and studied in connection with extinction transitions, in:

"Bacterial range expansions on a growing front: Roughness, Fixation, and Directed Percolation,"

J. Horowitz & M. Kardar PRE 99, 042134 (2019) (off-line)

yellow ball Ignoring invasion front shape, one possible geometry is a Circular Arc:

                            

yellow ball Another morphology is a Composite Bulge joining the flat front at a fixed slope:

                

 yellow ball Positive slopes occur for  slower mutant growth, leading to V-shaped Dents:

                  

This is somewhat surprising, as slower growth of isolated colonies suggests that they would lose out in competition.

However, such a V-shaped dent, with take-over of a slower growing mutant was observed recently:

"Slow expanders invade by forming dented fronts in microbial colonies,"

Hyunseok Lee, J. Gore1 and K.S. Korolev, PNAS 119, e2108653119.

(Different morphologies obtained through "geometric growth" rules)

red ball Phase diagram of possible growth morphologies: