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D. Ghersi
Cellular automata
They consist of a discrete lattice of sites called
CELLS
.
Each site takes on a finite set of possible values (red or white,0 or 1).
The value of each site evolves according to the same
deterministic
rules.
The rules for the evolution of a site depend only
on a local neighborhood of sites around it.
They evolve in discrete time steps.
Cellular Automata
consider discrete events and work from them to capture their consequences and
delineate the whole phenomenon.
Wolfram classical rules
Università di Genova
C.Calcagno

D. Ghersi
Conway's Game of Life
Rules
Survivals
Every counter with two or three neighboring counters survives for the next generation.
Deaths
Each counter with four or more neighbors dies (is removed) from overpopulation. Every counter with one
neighbor or none dies from isolation.
Births
Each empty cell adjacent to exactly three neighbors

no more, no fewer

is a birth cell. A counter is placed on
it at the next move.
Università di Genova
C.Calcagno

D. Ghersi
Conway's Game of Life (2)
Università di Genova
C.Calcagno

D. Ghersi
Immsim: a modified cellular automaton
As classical cellular automata do, it consists of a discrete lattice of site,but it uses the grid only as the
playground
of the simulation.
The grid id populated by different entities, placed randomly in all the cells of the lattice.
More then one entity can be in a single sitee.
At every time step the entities in the same site can interact with each other according to probabilistic rules and
they move from site to site.
Università di Genova
C.Calcagno

D. Ghersi
The grid
Università di Genova
C.Calcagno

D. Ghersi
Immsim basic rules
Rules modified in Immsim
The value of each site evolves according to the same
probabilistic
rules.
The rules for the evolution of a site depend only
by the site itself.
Added rule
The entities move from site to site
Università di Genova
C.Calcagno

D. Ghersi
Interactions
Antibody

Antigen
B Cell (BCR)

Antigen
T Killer (TCR)

APC (MHC I)
T Helper (TCR)

APC (MHC II)
T Killer (TCR)

Infected Cell (MHC I)
B Cell (MHC II)

T Helper (TCR)
The entities represented in Immsim interact whith each other
Interactions can be divided in
specific
and
non specific
Specific
Non specific
APC

Antigen
Epithelial Cell

Antigen
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D. Ghersi
Interactions (2)
Interactions activate specific programmes for both the entities involved
Epitope
Peptide
Peptide processing by B
cells
MHC loading and MPC
MPC
TCR

MPC interaction
B cell activation
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C.Calcagno

D. Ghersi
Interactions and specificity
Receptors
are represented by bit strings
Bit strings
are 0' and 1' sequences
11001100
Since each bit can take one of two value we can say that two bit strings complement each other
(
perfect match
) if every 0 in one correspond to a 1 in the other and conversely.
11000110
00111001
Perfect match
11
1
00110
00
1
11001
Mismatch 1
Specific
interactions
use
specific
receptors
Università di Genova
C.Calcagno

D. Ghersi
Bitstrings representation
Base

2
Base

10
11000110
00111001
198
57
11111111
255=2
8

1
How to calculate a best match
of a n

bits specificity
element(SE):
(2
n

1)

SE
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C.Calcagno

D. Ghersi
Interactions: overview
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D. Ghersi
The core of the simulation
1) Load parameters
Cells (randomly on the grid)
Antigen Injection (randomly on the grid)
2) Populate the grid
3) Interactions between entities in a randomic order
4) Death
5) Birth
Age
T Killer
Virus
6) Diffusion
Università di Genova
C.Calcagno

D. Ghersi
The Affinity Function
Affinity Slope
Weight coefficients

Calculates binding

probabilities according to the matching bits

Its slope can be modulated using weight coefficients
Università di Genova
C.Calcagno

D. Ghersi
Affinity and number of receptors
Matching
bits
No. of
Receptors

+

+
16 bits simulation
16/16
1
13/16
3360+240+16+1
15/16
14/16
16+1
240+16+1
17
257
3617
(65536 possible receptors)
Università di Genova
C.Calcagno

D. Ghersi
IMMSIM and probability
IMMSIM is a
probabilistic
cellular automaton:
Every interaction is based on a probabilistic factor, usually proportional to affinity.
Every entitity diffuses on the grid in a stochastic way.
Many programs of differentiation are implemented according to probabilistic rules.
Simulations started with the same parameters set can lead to slightly different
results.
In IMMSIM, in order to study a phenomenon, we must perform statistical
analyses.
Università di Genova
C.Calcagno

D. Ghersi
IMMSIM and probability (2)
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