Cellular Automata Modeling of

overwhelmedblueearthAI and Robotics

Dec 1, 2013 (3 years and 6 months ago)

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Cellular Automata Modeling of
Network Motif Performance

Background on Biological networks


A major area of research


Networks play important role in intercellular
functions


Examples include gene regulatory networks and
signaling pathways



Network Motifs



building blocks of complex networks




simple sub graphs that appear more often


than would be expected in a random graph




found in biological & ecological networks,


electronic circuitry, & internet








Feed Forward Loop


One of the most prevalent motifs


Heavily involved in regulatory mechanisms and cell
differentiation


Contains a direct path between the source node and
target node, as well as a secondary path through an
intermediate node or nodes




Linear Chain


Feed
-
Forward Loop

Feed
-
Forward Motifs

Linear Chain

Feed
-
Forward Motifs

Feed
-
Forward Motifs

Feed
-
Forward Motifs

Feed
-
Forward Motifs

Feed Forward Motifs

Bi
-
Parallel

Tri
-
Parallel

A

B

C

D

E

H


G

F



J



I

Chart of all 10 motifs ordered by performance

My Project


Characterize the performance of motifs when
process constants are variable


Look for patterns of change between motifs


Motifs are modeled using Cellular Automata


Modeling Networks


Models are an effective
tool for analyzing complex
networks


Biological networks have
been modeled using
systems of differential
equations (ODEs)


Can be ineffective due to
a lack of experimental
data



Cellular Automata


A flexible alternative to ODEs


Can effectively model biological
networks


ODEs are deterministic,
Cellular
Automata

is stochastic


Can be very computationally
expensive


“Simple mathematical idealizations of natural systems”




-

Stephen Wolfram

Cellular Automata Simulation in progress

How Cellular Automata Works


A grid of cells (squares)


A set of ingredients
(agents)


A set of rules governing the
behaviors of the
ingredients

A

B

A

B

B

A

B

A

The Cellular Automata Grid

The Rules


An agent can only interact
with the cells in its Von
Neumann Neighborhood


Movement and joining
between agents is
controlled by probability
rules


Y

Y

X

Y

Y

A Von Neumann Neighborhood

Changing State


Probability rules govern agents’ changes of state


This is how enzyme kinetics are modeled


Equation: A + E


AE


BE


B + E


This is how transitions between nodes in network
motifs are modeled

A

E

A

E

A

E

B

E

Selection of CA Parameters


Fixed number of runs


Fixed grid size


Iterations stop at:

T = 90%S









Concentrations of each node in the grid






S I1 I2 T



500 500 500 100

The Simulations of the Linear Case






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k = 5, 25, 125, 625






E1 E2 E3

The Simulations of the Linear Case

Series 1






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k =
5
, 25, 125, 625






E1

E2 E3

The Simulations of the Linear Case

Series 1






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k = 5,
25
, 125, 625






E1

E2 E3

The Simulations of the Linear Case

Series 1






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k = 5, 25,
125
, 625






E1

E2 E3

The Simulations of the Linear Case

Series 1






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k = 5, 25, 125,
625






E1

E2 E3

The Simulations of the Linear Case

Series 2






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k =
5
, 25, 125, 625






E1
E2

E3

The Simulations of the Linear Case

Series 2






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k = 5,
25
, 125, 625






E1
E2

E3

The Simulations of the Linear Case

Series 2






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k = 5, 25,
125
, 625






E1
E2

E3

The Simulations of the Linear Case

Series 2






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k = 5, 25, 125,
625






E1
E2

E3

The Simulations of the Linear Case

Series 3






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k =
5
, 25, 125, 625






E1 E2
E3

The Simulations of the Linear Case

Series 3






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k = 5,
25
, 125, 625






E1 E2
E3

The Simulations of the Linear Case

Series 3






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k = 5, 25,
125
, 625






E1 E2
E3

The Simulations of the Linear Case

Series 3






S I1 I2 T



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



k = 5, 25, 125,
625






E1 E2
E3

Feed Forward Motifs

Bi
-
Parallel

Tri
-
Parallel

A

B

C

D

E

H


G

F



J



I


Case H



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



4) S + E4 SE4 T + E4



5) I1 + E5 I1E5 T + E5



k = 5, 25, 125, 625, 3125













Case H: Series 1



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



4) S + E4 SE4 T + E4



5) I1 + E5 I1E5 T + E5






k =

5, 25, 125, 625, 3125



Performance range:
1246
-

1271

















Case H: Series 2



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



4) S + E4 SE4 T + E4



5) I1 + E5 I1E5 T + E5






k =

5, 25, 125, 625, 3125



Performance range:
1250
-

1264

















Case H: Series 3



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



4) S + E4 SE4 T + E4



5) I1 + E5 I1E5 T + E5






k =

5, 25, 125, 625, 3125



Performance range:
1788
-

2891

















Case H: Series 4



1) S + E1 SE1 I1 + E1



2) I1 + E2 I1E2 I2 + E2



3) I2 + E3 I2E3 T + E3



4) S + E4 SE4 T + E4



5) I1 + E5 I1E5 T + E5






k =

5, 25, 125, 625, 3125



Performance range:
1694
-

2230

















Future Directions


Analyze collected data


Run Simulations on larger feed forward architectures.


Different Scheme using Cellular Automata


Verify Model with ODEs



Any Questions?