Transcript Modelling And Observing Biology Matteo Cavaliere and Sean Sedwards Microsoft Research – University of Trento Centre for Computational and Systems Biology.

Modelling And Observing Biology
Matteo Cavaliere and Sean Sedwards
Microsoft Research – University of Trento
Centre for Computational and Systems Biology
Microsoft Research – University of Trento
Centre for Computational and Systems Biology
Computational biology
 Using biology to compute, e.g. DNA computing
 Modelling biology as a computational paradigm
Systems biology
 Modelling biological systems
 Specifically concerned with interactions
Microsoft Research – University of Trento
Centre for Computational And Systems Biology
Biological experiments are time consuming
Goal to provide ‘in-silico’ experimentation
Current tools based on
 process calculi, e.g. π-calculus
 formal language, e.g. P-systems
 model checking
Develop new tools with better abstractions
Our Inspiration And Challenge
“Quegli che pigliavano
per altore altro che la
natura maestra de‘
maestri s'affaticavano
invano”
Leonardo Da Vinci
“Those who took other
inspiration than from
nature, master of
masters, were labouring
in vain.”
Membrane Systems (P-systems)
Originally a computational paradigm introduced
in 1998*
Inspired by the structure and function
of biological cells
Based on formal language theory, using
concurrent multiset rewriting
Very adaptable: now many variants
*Gh. Păun. Computoing with Membranes, Journal of Computer and System Science, Vol. 61, No. 1, August 2000, pp. 108-143.
A Membrane System
hierarchical system
of compartments
with membranes
multisets of floating
objects local to regions
a
a
b
a a
ab
b
c c
a
b+aa+c
a+bc
b+cb+a
system
environment
a+bc
multisets of objects
a attached to membranes
ab
local evolution rules
based on formal
language rewriting
Our Model
Over one third of the human genome codes for
membrane proteins
Our model is an hierarchy of compartments
enclosed by membranes having three layers:
inner surface
proteins
integral
proteins
outer surface
proteins
We explicitly model peripheral and integral
membrane proteins
Our Model
To model biology we require rules for:
Rewriting of objects
 to model chemical reactions
Attachment of objects to membrane
 to alter membrane configuration
Movement of objects
 conditional on membrane configuration
 to model e.g. endo- and exocytosis
Rewriting
Rules used to generate languages:
[uv]
tuv  tvv
[ a  ab ]
a  ab  abb  abbb  ….
[ xy  xx ]
xyyy  xxyy  xxxy  xxxx
Behave like chemical reactions:
x+y2x
Multisets
A multiset is a set where each element may
have a multiplicity
{a, a, a, b, b, c, c, c, c} = {(a,3), (b,2), (c,4)}
A multiset can be represented by a string
{(a,3), (b,2), (c,4)} = aaabbcccc
A chemical solution can be considered a
multiset of molecules
Evolution Rules
[ a  b ]1
2
b
a
u
aa
1
v
u
v
Evolution Rules
[ a  b ]1
2
b
a
u
v
aa
u
2
b
a
uv
bb
1
v
1
Membrane Rules
General membrane rule:
[ w ]u|v|x + z  [ w′ ]u′|v′|x′ + z′
w,u,v,x,z,w′,u′,v′,x′,z′  V*
w = prior multiset of floating objects
u = prior multiset attached to inner surface of membrane
v = prior multiset integral to membrane
x = prior multiset attached to external surface
z = prior multiset of external floating objects
w′ = posterior multiset of floating objects
u′ = posterior multiset attached to inner surface
v′ = posterior multiset integral to membrane
x′ = posterior multiset attached to external surface
z′ = posterior multiset of external floating objects
Attachment Rules
1
1
[ a ]u|v|  [ ]a'u'|v'|
2
1
b
[ ] |v|x a  [ ] |v‘|x'a'
2
2
v x
a
aa
u v
Attachment Rules
1
1
[ a ]u|v|  [ ]a'u'|v'|
[ ] |v|x a  [ ] |v‘|x'a'
2
2
2
attachment
dependent on
membrane markings
1
b
v x
a
aa
u v
2
1
b
v x
a
a
a'u' v'
Attachment Rules
1
1
[ a ]u|v|  [ ]a'u'|v'|
2
1
b
v x
[ ] |v|x a  [ ] |v‘|x'a'
2
2
a
aa
u v
2
1
2
1
b
b
v' x'a'
a
a'u' v'
v x
a
a
a'u' v'
Movement Rules
1
1
[ a ]u|v|  [ ]u'|v'|
+ a'
2
1
b
[ ] |v|x a  [ a' ] |v‘|x'
2
2
v x
a
aa
u v
Movement Rules
1
1
[ a ]u|v|  [ ]u'|v'|
+ a'
1
2
b
[ ] |v|x a  [ a' ] |v‘|x'
2
2
movement dependent
on membrane
markings
v x
a
aa
u v
1
2
b
v x
aa
a
u' v'
Movement Rules
1
1
[ a ]u|v|  [ ]u'|v'|
+ a'
2
1
b
v x
[ ] |v|x a  [ a' ] |v‘|x'
2
2
a
aa
u v
2
1
2
1
b
ba
v x
v' x'
a
aa
a'u' v'
a
a'u' v'
Evolution Semantics
Maximal parallel
all possible rules applied at the same time
universal power but properties undecidable
no apparent biological relevance
Free parallel
an arbitrary number of rules applied
power equivalent to matrix grammar w/o a/c
reachability of configurations / markings is decidable
chemical semantics are sequential (specific case)
Discrete Stochastic Evolution
Associate a reaction rate to each rule
Use Gillespie algorithm to select:


which rule occurs next
when it occurs
Time t=0
Stochastically select rule r to occur next with delay dt,
else quit if no rule can be applied.
Execute rule r, t := t + dt.
Algorithm Applied To Membranes
Conceptually…
Every object in the system is mapped to a new floating
object in a new system with a single compartment.
Each new object has a subscript which uniquely defines
its previous containment and attachment.
2
b
a
u
aa
1
b2 u2,inner x2,outer
x
a1a1a1 u1,inner x1,outer
u
x
Algorithm Applied To Membranes
Every rule in the system is mapped to a new evolve rule,
using the same mappings as the objects
1
1
[ a ]u|v|
 [ ]au|v|
[ a1u1,innerv1,integral  a1,inneru1,innerv1,integral ]
[ ] 2|v|x a  [ a ] 2|v|x
[ a1v2,integralx2,outer  a2v2,integralx2,outer ]
The stochastic algorithm is then applied to the new
system comprising the mapped rules and objects in a
single compartment
Simulator Rule Syntax
Standard evolution rule:
[ab]
a,b  V*
a={a1,a2,a3}, b={b1,b2}
Simulator evolution rule:
a1 + a2 + a3 -> b1 + b2
Circadian Clock
alphabet definition
object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR
AR
rule circadian_clock
rule
definitions
1
{
0.2
gene_A 50-> MA + gene_A
1
2
A+gene_A 1-> A_gene_A
A_gene_A 500-> MA + A_gene_A
A
R
+
gene_R 0.01-> MR + gene_R
5
A_gene_R 50-> MR + A_gene_R
0.5
10
50
MA 50-> A
MA
MR
MR 5-> R
A+R 2-> AR
0.01
50
50
average reaction rate
500
AR 1-> R
A
A
+
+
A 1-> 0A
R 0.2-> 0R
A
A
MA 10-> 0MA
gene_A
1 A_gene_A gene_R
1 A_gene_R
MR 0.5-> 0MR
A_gene_R 100-> A+gene_R
50
100
A+gene_R 1-> A_gene_R
A_gene_A 50-> A+gene_A
Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002
}
system 1 gene_A, 1 gene_R, circadian_clock
evolve 0-150000
plot A, R
initial system configuration
objects to observe
observation period
Circadian Clock
object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR
rule circadian_clock
{
gene_A 50-> MA + gene_A
A+gene_A 1-> A_gene_A
A_gene_A 500-> MA + A_gene_A
gene_R 0.01-> MR + gene_R
A_gene_R 50-> MR + A_gene_R
MA 50-> A
MR 5-> R
A+R 2-> AR
AR 1-> R
A 1-> 0A
R 0.2-> 0R
MA 10-> 0MA
MR 0.5-> 0MR
A_gene_R 100-> A+gene_R
A+gene_R 1-> A_gene_R
A_gene_A 50-> A+gene_A
}
system 1 gene_A, 1 gene_R, circadian_clock
evolve 0-150000
plot A, R
AR
1
1
0.2
2
A
R
+
5
10
0.5
50
MA
A
50
500
+
MR
A
0.01
50
+
A
A
gene_A
1
50
A_gene_A
gene_R
1 A_gene_R
100
Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002
Circadian Clock
object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR
rule circadian_clock
{
gene_A 50-> MA + gene_A
A+gene_A 1-> A_gene_A
A_gene_A 500-> MA + A_gene_A
gene_R 0.01-> MR + gene_R
A_gene_R 50-> MR + A_gene_R
MA 50-> A
MR 5-> R
A+R 2-> AR
AR 1-> R
A 1-> 0A
R 0.2-> 0R
MA 10-> 0MA
MR 0.5-> 0MR
A_gene_R 100-> A+gene_R
A+gene_R 1-> A_gene_R
A_gene_A 50-> A+gene_A
}
system 1 gene_A, 1 gene_R, circadian_clock
evolve 0-150000
plot A, R
AR
1
1
0.2
2
A
R
+
5
10
0.5
50
MA
A
50
500
+
MR
A
0.01
50
+
A
A
gene_A
1
50
A_gene_A
gene_R
1 A_gene_R
100
Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002
Circadian Clock
object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR
rule circadian_clock
{
gene_A 50-> MA + gene_A
A+gene_A 1-> A_gene_A
A_gene_A 500-> MA + A_gene_A
gene_R 0.01-> MR + gene_R
A_gene_R 50-> MR + A_gene_R
MA 50-> A
MR 5-> R
A+R 2-> AR
AR 1-> R
A 1-> 0A
R 0.2-> 0R
MA 10-> 0MA
MR 0.5-> 0MR
A_gene_R 100-> A+gene_R
A+gene_R 1-> A_gene_R
A_gene_A 50-> A+gene_A
}
system 1 gene_A, 1 gene_R, circadian_clock
evolve 0-150000
plot A, R
AR
1
1
0.2
2
A
R
+
5
10
0.5
50
MA
A
50
500
+
MR
A
0.01
50
+
A
A
gene_A
1
50
A_gene_A
gene_R
1 A_gene_R
100
Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002
Circadian Clock
object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR
rule circadian_clock
{
gene_A 50-> MA + gene_A
A+gene_A 1-> A_gene_A
A_gene_A 500-> MA + A_gene_A
gene_R 0.01-> MR + gene_R
A_gene_R 50-> MR + A_gene_R
MA 50-> A
MR 5-> R
A+R 2-> AR
AR 1-> R
A 1-> 0A
R 0.2-> 0R
MA 10-> 0MA
MR 0.5-> 0MR
A_gene_R 100-> A+gene_R
A+gene_R 1-> A_gene_R
A_gene_A 50-> A+gene_A
}
system 1 gene_A, 1 gene_R, circadian_clock
evolve 0-150000
plot A, R
AR
1
1
0.2
2
A
R
+
5
10
0.5
50
MA
A
50
500
+
MR
A
0.01
50
+
A
A
gene_A
1
50
A_gene_A
gene_R
1 A_gene_R
100
Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002
Circadian Clock
object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR
rule circadian_clock
{
gene_A 50-> MA + gene_A
A+gene_A 1-> A_gene_A
A_gene_A 500-> MA + A_gene_A
gene_R 0.01-> MR + gene_R
A_gene_R 50-> MR + A_gene_R
MA 50-> A
MR 5-> R
A+R 2-> AR
AR 1-> R
A 1-> 0A
R 0.2-> 0R
MA 10-> 0MA
MR 0.5-> 0MR
A_gene_R 100-> A+gene_R
A+gene_R 1-> A_gene_R
A_gene_A 50-> A+gene_A
}
system 1 gene_A, 1 gene_R, circadian_clock
evolve 0-150000
plot A, R
AR
1
1
0.2
2
A
R
+
5
10
0.5
50
MA
A
50
500
+
MR
A
0.01
50
+
A
A
gene_A
1
50
A_gene_A
gene_R
1 A_gene_R
100
Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002
Circadian Clock Simulation
250
A
200
150
R
100
50
0
0
50
100
150
200
250
hours
Oscillations with period c24 hours
In-silico Knockout Experiment
object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR
rule circadian_clock
{
gene_A 50-> MA + gene_A
A+gene_A 1-> A_gene_A
A_gene_A 500-> MA + A_gene_A
gene_R 0.01-> MR + gene_R
A_gene_R 50-> MR + A_gene_R
MA 50-> A
MR 5-> R
A+R 2-> AR
AR 1-> R
A 1-> 0A
R 0.2-> 0R
MA 10-> 0MA
MR 0.5-> 0MR
knockout gene for R
A_gene_R 100-> A+gene_R
at step 50000
A+gene_R 1-> A_gene_R
A_gene_A 50-> A+gene_A
}
system 1 gene_A, 1 gene_R, -1 gene_R@50000, -1 A_gene_R@50000, circadian_clock
evolve 0-150000
plot A, R
Knockout Simulation Results
300
A
250
200
R
150
100
50
0
0
20
40
60
80
100
120
140
160
hours
Switch off gene for R
Hidden Pathway
250
200
150
100
50
AR
R
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
hours
Residual R persists due to slow decay of AR
Membrane Rule Syntax
Model attach rules:
[ a ]u|v|  [ ]a'u'|v'|
[ ] |v|x a  [ ] |v'|x'a'
Simulator attach rules:
a,u,v,x,a',u',v',x'  V
attached
a1 + u1|v1| -> a2,u2|v2|
|v1|x1 + a1 -> |v2|x2,a2
inside
outside
membrane
Move Rule Syntax
Model move rules:
[ a ]u|v|  [ ]u'|v'| a'
[ ] |v|x a  [ a ] |v'|x'
a,u,v,x,a',u',v',x'  V
Simulator move rules:
a1 + u1|v1| -> u2|v2| + a2
|v1|x1 + a1 -> a2 + |v2|x2
inside
outside
inside
outside
Yeast G-protein Cycle
object L,R,RL,Gd,Gbg,Gabg,Ga
rule g_cycle {
|| 4-> |R|
|R| + L 3.32e-18-> |RL|
|RL| 0.01-> |R| + L
|RL| 0.004-> RL + ||
|R| 4.0e-4-> R + ||
Gabg + |RL| 1.0e-5-> Ga, Gbg + |RL|
Gd + Gbg 1-> Gabg
Ga 0.11-> Gd
}
rule vac_rule {
|| + R 4.0e-4-> R + ||
|| + RL 0.004-> RL + ||
}
compartment vacuole [vac_rule]
compartment cell [vacuole, 3000 Gd, 3000 Gbg, 7000 Gabg, g_cycle : |10000 R|]
system cell, 6.022e17 L
evolve 0-600000
plot cell[Gd,Gbg,Gabg,Ga:|R,RL|]
Yi, Kitano, Simon, PNAS, 100, 19, 2003
Yeast G-protein Cycle
object L,R,RL,Gd,Gbg,Gabg,Ga
rule g_cycle {
|| 4-> |R|
|R| + L 3.32e-18-> |RL|
|RL| 0.01-> |R| + L
|RL| 0.004-> RL + ||
|R| 4.0e-4-> R + ||
Gabg + |RL| 1.0e-5-> Ga, Gbg + |RL|
Gd + Gbg 1-> Gabg
Ga 0.11-> Gd
}
rule vac_rule {
|| + R 4.0e-4-> R + ||
|| + RL 0.004-> RL + ||
}
compartment vacuole [vac_rule]
compartment cell [vacuole, 3000 Gd, 3000 Gbg, 7000 Gabg, g_cycle : |10000 R|]
system cell, 6.022e17 L
evolve 0-600000
plot cell[Gd,Gbg,Gabg,Ga:|R,RL|]
Yeast G-protein Cycle
object L,R,RL,Gd,Gbg,Gabg,Ga
rule g_cycle {
|| 4-> |R|
|R| + L 3.32e-18-> |RL|
|RL| 0.01-> |R| + L
|RL| 0.004-> RL + ||
|R| 4.0e-4-> R + ||
Gabg + |RL| 1.0e-5-> Ga, Gbg + |RL|
Gd + Gbg 1-> Gabg
Ga 0.11-> Gd
}
rule vac_rule {
|| + R 4.0e-4-> R + ||
|| + RL 0.004-> RL + ||
}
compartment vacuole [vac_rule]
compartment cell [vacuole, 3000 Gd, 3000 Gbg, 7000 Gabg, g_cycle : |10000 R|]
system cell, 6.022e17 L
evolve 0-600000
plot cell[Gd,Gbg,Gabg,Ga:|R,RL|]
Yeast G-protein Cycle
object L,R,RL,Gd,Gbg,Gabg,Ga
rule g_cycle {
|| 4-> |R|
|R| + L 3.32e-18-> |RL|
|RL| 0.01-> |R| + L
|RL| 0.004-> RL + ||
|R| 4.0e-4-> R + ||
Gabg + |RL| 1.0e-5-> Ga, Gbg + |RL|
Gd + Gbg 1-> Gabg
Ga 0.11-> Gd
}
rule vac_rule {
|| + R 4.0e-4-> R + ||
|| + RL 0.004-> RL + ||
}
compartment vacuole [vac_rule]
compartment cell [vacuole, 3000 Gd, 3000 Gbg, 7000 Gabg, g_cycle : |10000 R|]
system cell, 6.022e17 L
evolve 0-600000
plot cell[Gd,Gbg,Gabg,Ga:|R,RL|]
Yeast G-protein Cycle
object L,R,RL,Gd,Gbg,Gabg,Ga
rule g_cycle {
|| 4-> |R|
|R| + L 3.32e-18-> |RL|
|RL| 0.01-> |R| + L
|RL| 0.004-> RL + ||
|R| 4.0e-4-> R + ||
Gabg + |RL| 1.0e-5-> Ga, Gbg + |RL|
Gd + Gbg 1-> Gabg
Ga 0.11-> Gd
}
rule vac_rule {
|| + R 4.0e-4-> R + ||
|| + RL 0.004-> RL + ||
}
compartment vacuole [vac_rule]
compartment cell [vacuole, 3000 Gd, 3000 Gbg, 7000 Gabg, g_cycle : |10000 R|]
system cell, 6.022e17 L
evolve 0-600000
plot cell[Gd,Gbg,Gabg,Ga:|R,RL|]
Yeast G-protein Cycle
object L,R,RL,Gd,Gbg,Gabg,Ga
rule g_cycle {
|| 4-> |R|
|R| + L 3.32e-18-> |RL|
|RL| 0.01-> |R| + L
|RL| 0.004-> RL + ||
|R| 4.0e-4-> R + ||
Gabg + |RL| 1.0e-5-> Ga, Gbg + |RL|
Gd + Gbg 1-> Gabg
Ga 0.11-> Gd
}
rule vac_rule {
|| + R 4.0e-4-> R + ||
|| + RL 0.004-> RL + ||
}
compartment vacuole [vac_rule]
compartment cell [vacuole, 3000 Gd, 3000 Gbg, 7000 Gabg, g_cycle : |10000 R|]
system cell, 6.022e17 L
evolve 0-600000
plot cell[Gd,Gbg,Gabg,Ga:|R,RL|]
Yeast G-protein Cycle
object L,R,RL,Gd,Gbg,Gabg,Ga
rule g_cycle {
|| 4-> |R|
|R| + L 3.32e-18-> |RL|
|RL| 0.01-> |R| + L
|RL| 0.004-> RL + ||
|R| 4.0e-4-> R + ||
Gabg + |RL| 1.0e-5-> Ga, Gbg + |RL|
Gd + Gbg 1-> Gabg
Ga 0.11-> Gd
}
rule vac_rule {
|| + R 4.0e-4-> R + ||
|| + RL 0.004-> RL + ||
}
compartment vacuole [vac_rule]
compartment cell [vacuole, 3000 Gd, 3000 Gbg, 7000 Gabg, g_cycle : |10000 R|]
system cell, 6.022e17 L
evolve 0-600000
plot cell[Gd,Gbg,Gabg,Ga:|R,RL|]
Yeast G-protein Cycle
object L,R,RL,Gd,Gbg,Gabg,Ga
rule g_cycle {
|| 4-> |R|
|R| + L 3.32e-18-> |RL|
|RL| 0.01-> |R| + L
|RL| 0.004-> RL + ||
|R| 4.0e-4-> R + ||
Gabg + |RL| 1.0e-5-> Ga, Gbg + |RL|
Gd + Gbg 1-> Gabg
Ga 0.11-> Gd
}
rule vac_rule {
|| + R 4.0e-4-> R + ||
|| + RL 0.004-> RL + ||
}
compartment vacuole [vac_rule]
compartment cell [vacuole, 3000 Gd, 3000 Gbg, 7000 Gabg, g_cycle : |10000 R|]
system cell, 6.022e17 L
evolve 0-600000
plot cell[Gd,Gbg,Gabg,Ga:|R,RL|]
Yeast G-protein Cycle
10000
object L,R,RL,Gd,Gbg,Gabg,Ga
8000
rule g_cycle {
|| 4-> |R|
|R| + L 3.32e-18-> |RL|
6000
|RL| 0.01-> |R| + L
|RL| 0.004-> RL + ||
|R| 4.0e-4-> R + ||
Gabg + |RL| 1.0e-5-> Ga, Gbg + |RL| 4000
Gd + Gbg 1-> Gabg
Ga 0.11-> Gd
2000
}
rule vac_rule {
|| + R 4.0e-4-> R + ||
R
0
|| + RL 0.004-> RL + ||
Gd
0
100
200
300
400
}
compartment vacuole [vac_rule]
compartment cell [vacuole, 3000 Gd, 3000 Gbg, 7000 Gabg, g_cycle : |10000 R|]
system cell, 6.022e17 L
evolve 0-600000
plot cell[Gd,Gbg,Gabg,Ga:|R,RL|]
Gabg
RL
Gbg
Ga
500
600
Composing Systems
Electronic components designed to be
compositional
components
sub-circuits
functional
blocks
circuits
electronic systems
Decomposing Biology
We would like biology to be the same…
Biology
Biology is not designed to be decomposed
Levels Of Abstraction
Problem:
Biological systems are maximally complex
Impossible to know everything about structure
Difficult to model at a molecular level with partial
information
Difficult to find perfect level of abstraction
Possible solution:
model at an arbitrary level of abstraction using a formal
observer
Computing By Observing
Possible to compute by simply observing the evolution
of a system*
Universal power from a FSA observing a PDA

get everything by just changing the observer
*M. Cavaliere, P. Frisco, H. Hoogeboom, Computing by Only Observing, Lecture Notes in Computer Science 4036, Springer-Verlag.
Computing By Observing
Possible to compute by simply observing the evolution
of a system*
Universal power from a FSA observing a PDA

get everything by just changing the observer
system
evolution
G
B
observer
R
B RB G GRB RG
observation
*M. Cavaliere, P. Frisco, H. Hoogeboom, Computing by Only Observing, Lecture Notes in Computer Science 4036, Springer-Verlag.
Observing Biology
Reduce complexity by working modulo an observer
Biological system modulo observer
Biological system
observer
Objectives
Further develop simulation language based on
rewriting, compartments and membranes
Add features to
 enable deterministic and hybrid simulations
 generate information, e.g. model checking
 compose compartments,
e.g. fission and fusion
 work with non-atomic objects, e.g. complexes
 more accurately model membranes
Develop ideas of working modulo an observer
Acknowledgements
Corrado Priami
Tommaso Mazza
www.msr-unitn.unitn.it/downloads.php
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