Quantitative study of pattern formation on a density-dependent motility biological system

Abstract

Quantitative biology is an emerging field that attracts intensive research interests.

Pattern formation is a widely studied topic both in biology and physics.

Scientists have been trying to figure out the basic principles behind the fascinating

patterns in the nature. It’s still difficult to lift the complex veil on the

underling mechanisms, especially in biology, although lots of the achievements

have been achieved. The new developments in synthetic biology provide a different

approach to study the natural systems, test the theories, and develop

new ones. Biological systems have many unique features different from physics

and chemistry, such as growth and active movement. In this project, a link

between cell density and cell motility is established through cell-cell signaling.

The genetic engineered Escherichia coli cell regulates its motility by sensing

the local cell density. The regulation of cell motility by cell density leads to

sequential and periodical stripe patterns when the cells grow and expand on a

semi-solid agar plate. This synthetic stripe pattern formation system is quantitative

studied by quantitative measurements, mathematical modeling and

theoretical analysis.

To characterize the stripe pattern, two novel methods have been developed

to quantify the key parameters, including cell growth, spatiotemporal cell density

profile and cell density-dependent motility, besides the standard molecular

biological measurements.

To better understand the underlying principle of the stripe pattern formation,

a quantitative model is developed based on the experiments. The detailed

dynamic process is studied by computer simulation. Besides, the model predicts

that the number of stripes can be tuned by varying the parameters in

the system. This has been tested by quantitatively modulation of the basal

expression level of a single gene in the genetic circuit.

Moreover, theoretical analysis of a simplified model provides us a clear picture

of the stripe formation process. The steady state traveling wave solution

is obtained, which leads to an analytic ansatz that can determine the phase

boundary between the stripe and the no-stripe phases.

This study does not only provide a quantitative understanding about the

novel mechanism of stripe pattern formation, but also sets an good example

of quantitative studies in biology. The techniques, methods and knowledge

gleaned here may be applied in various interdisciplinary fields.