The unifying element in the above cases was the presence of
force-fields affecting the dynamic behavior of the agents. The fields
were time-invariant and their spatial dependence was of the formFFd¼FFoed:where FFdis the force-field strength at distance d from the source
FFo.
The numerical resolution of such space dependence was
directly proportional to the granularity of the agents’ world
(the grid).
In the detailed description of each case the research problem in
the background will be briefly sketched, as well as the simple rules
defining the behavior of the single agents and the typical results
provided by the simulations.2.1 Cell Shapes
and Fields
2.1.1 The Problem
The morphofunctional changes within a population of initially
similar elements can be the result of coexisting endogeneous
(genetic) and/or exogeneous (environmental) factors. The quanti-
fication of their relative importance remains of crucial interest, due
to the obvious functional—pathological modifications linked to the
morphological changes.
According to a crude but quite useful approximation, switching
from one conformation (C 1 ) to another (C 2 ), namelyC 1 !C 2 , can
be described by a simple first-order process. The rate of the process,
V1,is ruled by a kinetic constantk 1 , namelyV 1 ¼k 1 [C 1 ], where
the square brackets indicate molar concentration. If the switch is
reversible, the same reasoning applies to the reverse process,
C 1 J C 2 , leading to an equilibrium condition when
V 1 ¼k 1 [C 1 ]¼V 2 ¼k 2 [C 2 ]. Thus, under equilibrium
conditions theC 1 /C 2 ratio is given byk 2 /k 1.2.1.2 The Model The interconversion from a “regular,” yellow (Y) to a “spiky,” blue
(B) shape, within a population of up to several thousand cells is
modeled as a standard biochemical equilibrium between two con-
formations [13] influenced by:
l Chemical factors (“apparent” kinetic constants for the B!Y and
Y!B conversions).
l Physical factors (external force-fields).
The “apparent” kinetic constants include an “intrinsic” factor
as well as two “environmental” factors regulated by two specific
force-fields. Each of the two force-fields influences only one of the
two kinetic constants.
Figure2 shows how a population of agents all in the same
yellow state at time¼t 0 (panel A), undergoes a reversible shift to
another (blue) state, reaching different equilibria ruled by different
k 1 :k 2 ratios. Such ratios are 1:1; 0.7:0.3 and 0.3:0.7 in panels B, C310 Alfredo Colosimo