Amyloid protein exists in two forms, soluble and fibrous. It is secreted by neurons in the soluble form, diffuses in the soluble form and can be changed to a fibrous form depending on its local concentration, and on the interaction between the soluble and fibrous forms. Amyloid protein is removed from the environment due to uptake by microglia.
The program sets a limit on the concentration of fibers called MAXFIBERS. This programmer defined constant is used in several of the fiber processes. The current value of MAXFIBERS is 150.
Initially, soluble amyloid is secreted from
neurons in the center of the environment.
Amyloid fibers are also placed randomly in the domain
based on the initial fiber
occupancy parameter, p. In other words, for
each grid space, a uniformly distrubed random variable between 0 and 1
is generated and if its value is less than p, then a random
concentration of fibers is placed in the grid space. The random
concentration of fibers is uniformly distributed between 0 and
MAXFIBERS.
When a neuron's internal concentration of IL-1B exceeds
the source triggering level the Neuron
secretes soluble amyloid
protein at its grid location. The rate of
secretion, r, is determined as a function of the
source concentration parameter, I. Specifically,
Soluble amyloid diffuses according to the diffusion
properties discussed above. Initially, the diffusion coefficient
equals the diffusivity parameter throughout. However,
astrocyte blocking may reduce the
diffusion coefficient in specific regions.
Soluble amyloid is transformed to amyloid fibers within a grid space in two possible ways. If there are already some fibers in the grid space, these can grow based on the sol to fiber transition rate. If there are no fibers present in the grid space, then new fiber nucleation based on the presence of fibers in the surrouding grid spaces must be considered. In either case, the concentration of soluble amyloid in the grid space must exceed the critical sol-AB for fibers parameter, for fiber transitions to occur.
When fibers are present, growth occurs at a rate proportional to
the product of the average surrounding fiber concentration, F
(a weighted average with the center fibers counting more than the
immediately surrounding fibers by a programmer defined constant,
WEIGHT -- currently, WEIGHT=2.0, meaning that fibers in
the center count twice as much as surrounding fibers), and the
difference between the concentration of soluble amyloid, s,
within the grid space and the critical sol-AB for fibers
parameter, b. If f is the concentration of fibers
in the grid space, then
In the case where no fibers are present in the grid space under
consideration, the grid space may still gain fibers if no astrocytes
occupy the space and the concentration of soluble amyloid exceeds
the critical sol-AB for fibers parameter. This is done
through the process of fiber nucleation. Fiber
nucleation depends on the weighted average of concentration of fibers
surrounding the grid space, F, the maximum fiber concentration,
MAXFIBERS, and the new fiber nucleation effectiveness
parameter, n. These terms are combined to give a "probability"
that the site undergoes nucleation, p = n*(F/MAXFIBERS).
Every macro time step, nucleation is
tested for via a Monte Carlo technique. Specifically, a uniformly
distributed random number between 0 and 1 is generated. If its
value is less than p, then nucleation occurs and the rate
of fiber growth is determined as described in the preceding
paragraph.