Thimo Rohlf: Robust pattern formation and development under noise and cell flow

Self-organized pattern formation and expression domain control under noise

Thimo Rohlf and Stefan Bornholdt

Abstract

The JAVA applet below simulates a new non-equilibrium model for spatial pattern formation motivated by animal morphogenesis on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability . Information is transmitted through the system via particle-like excitations whose collective dynamics result in pattern formation and control, without need for long-range gradients . Here, a simple problem of domain formation is addressed by this model in an implementation as stochastic cellular automata. One observes stable pattern formation, even in the presence of noise and cell flow. Noise stabilizes the system through the production of quasi-particles that control the position of the domain boundary. Self-organized boundaries become sharp for large system with fluctuations vanishing with a power of the system size. Pattern proportions are scale-independent with system size. Pattern formation is stable over large parameter ranges. A first order phase transition is observed for vanishing noise and a second order phase transition at increasing cell flow. The pattern formation mechanism studied here is very general and not limited to cellular automata. In particular, implementations as regulatory networks work as well and do not differ in complexity from regulatory circuits observed in the cell.

Reference: cond-mat0312366

How to use the applet:

Buttons and text fields:

reinitialize (button): starts system dynamics from a random initial configuration.

system size (text field): varies the number N_C of cells the system consists of. You may enter values between 0 and 500 and press "return" to set the new system size.

N_C++/N_C-- (button): increases/decreases the number of cells.

error rate r_e (text field): sets the rate r_e of stochastic update errors. Ordered dynamics is obtained for values 0 <= r_e < 1/2.

r_e++/r_e-- (button): increases/decreases the error rate.

cell flow rate r_f (text field): sets the rate r_f of cell flow. To obtain a domain boundary, enter values between 0 and r_e.

r_f++/r_f-- (button): increases/decreases the cell flow rate.

direction (button): changes the dircetion of cell flow.

animation speed (text field): enter values between 1 and 100 to set the animation speed.

Markers on the bottom bar: The green mark indicates the average boundary position as calculated from mean field theory. The moving white mark indicates velocity and direction of cell flow.