Modelling And Observing Biology - microsoft.com

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. -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. Pun. 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 ab b c c a b+aa+c a+bc b+cb+a system environment

a+bc 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:

[uv] tuv tvv [ a ab ] a ab abb abbb . [ xy xx ] xyyy xxyy xxxy xxxx Behave like chemical reactions: x+y2x 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 [ab]1 2 b a u aa 1 v u

v Evolution Rules [ab]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 u|v| [a] 1 a'u'|v'| [ ] 2 1 b [ ] 2 |v|x a[ ]

2 |v|x'a' v x a aa u v Attachment Rules 1 u|v| [a] [ ] 2 |v|x 1 a'u'|v'| [ ] a[ ] 2 |v|x'a' 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 u|v| [a] 1 a'u'|v'| [ ] 2 1

b [ ] 2 |v|x a[ ] v x 2 |v|x'a' a 2 aa 1 u v 2 1 b b v' x'a' a a'u' v'

v x a a a'u' v' Movement Rules 1 u|v| [a] 1 u'|v'| [ ] + a' 2 1 b [ ] 2 |v|x a [ a' ] 2 |v|x'

v x a aa u v Movement Rules 1 u|v| [a] 1 u'|v'| [ ] + a' 1 2 b [ ] 2 |v|x a [ a' ] 2 |v|x' v x

movement dependent on membrane markings a aa u v 1 2 b v x aa a u' v' Movement Rules 1 u|v| [a] 1 u'|v'| [ ] + a' 2

1 b [ ] 2 |v|x a [ a' ] v x 2 |v|x' a 2 aa 1 u v 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 u x a1a1a1 u1,inner x1,outer 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| 2 [ a1u1,innerv1,integral a1,inneru1,innerv1,integral ]

2 [ ] |v|x a [ a ] |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: [ab] a,b V* a={a1,a2,a3}, b={b1,b2} Simulator evolution rule: a1 + a2 + a3 -> b1 + b2 Circadian Clock alphabet definition object object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR rule rule circadian_clock circadian_clock rule definitions AR 1 {{ 0.2 gene_A gene_A 50-> 50-> MA MA ++ gene_A gene_A

1 2 A+gene_A A+gene_A 1-> 1-> A_gene_A A_gene_A A_gene_A 500-> A R A_gene_A 500-> MA MA ++ A_gene_A A_gene_A gene_R gene_R 0.01-> 0.01-> MR MR ++ gene_R gene_R + 5 A_gene_R A_gene_R 50-> 50-> MR MR ++ A_gene_R A_gene_R 0.5 10 50 MA MA 50-> 50-> AA MA MR MR MR 5-> 5-> RR

A+R A+R 2-> 2-> AR AR 0.01 50 50 average reaction rate 500 AR AR 1-> 1-> RR A A + + AA 1-> 1-> 0A 0A A A RR 0.2-> 0.2-> 0R 0R MA MA 10-> 10-> 0MA 0MA gene_A 1 A_gene_A gene_R 1 A_gene_R MR 0.5-> 0MR MR 0.5-> 0MR A_gene_R

A_gene_R 100-> 100-> A+gene_R A+gene_R 50 100 A+gene_R 1-> A_gene_R A+gene_R 1-> A_gene_R A_gene_A A_gene_A 50-> 50-> A+gene_A A+gene_A Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002 }} system system 11 gene_A, gene_A, 11 gene_R, gene_R, circadian_clock circadian_clock evolve evolve 0-150000 0-150000 initial system configuration plot plot A, A, RR objects to observe observation period Circadian Clock object object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR, gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,AA,R,AR

,R,AR rule rule circadian_clock circadian_clock {{ gene_A gene_A 50-> 50-> MA MA ++ gene_A gene_A A+gene_A 1-> A_gene_A A+gene_A 1-> A_gene_A A_gene_A A_gene_A 500-> 500-> MA MA ++ A_gene_A A_gene_A gene_R gene_R 0.01-> 0.01-> MR MR ++ gene_R gene_R A_gene_R A_gene_R 50-> 50-> MR MR ++ A_gene_R A_gene_R MA MA 50-> 50-> AA MR MR 5-> 5-> RR A+R

A+R 2-> 2-> AR AR AR AR 1-> 1-> RR AA 1-> 1-> 0A 0A RR 0.2-> 0.2-> 0R 0R MA 10-> 0MA MA 10-> 0MA MR MR 0.5-> 0.5-> 0MR 0MR A_gene_R 100-> A_gene_R 100-> A+gene_R A+gene_R A+gene_R 1-> A_gene_R A+gene_R 1-> A_gene_R A_gene_A A_gene_A 50-> 50-> A+gene_A A+gene_A }} system system 11 gene_A, gene_A, 11 gene_R,

gene_R, circadian_clock circadian_clock evolve evolve 0-150000 0-150000 plot plot A, A, RR AR 1 1 0.2 2 A R + 10 5 0.5 50 MA A 50 500

+ MR A 0.01 + A A gene_A 1 50 A_gene_A 50 gene_R 1 A_gene_R 100 Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002 Circadian Clock object object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR rule rule circadian_clock circadian_clock {{ gene_A

gene_A 50-> 50-> MA MA ++ gene_A gene_A A+gene_A 1-> A_gene_A A+gene_A 1-> A_gene_A A_gene_A A_gene_A 500-> 500-> MA MA ++ A_gene_A A_gene_A gene_R gene_R 0.01-> 0.01-> MR MR ++ gene_R gene_R A_gene_R A_gene_R 50-> 50-> MR MR ++ A_gene_R A_gene_R MA MA 50-> 50-> AA MR MR 5-> 5-> RR A+R A+R 2-> 2-> AR AR AR AR 1-> 1-> RR

AA 1-> 1-> 0A 0A RR 0.2-> 0.2-> 0R 0R MA 10-> 0MA MA 10-> 0MA MR MR 0.5-> 0.5-> 0MR 0MR A_gene_R 100-> A_gene_R 100-> A+gene_R A+gene_R A+gene_R 1-> A_gene_R A+gene_R 1-> A_gene_R A_gene_A A_gene_A 50-> 50-> A+gene_A A+gene_A }} system system 11 gene_A, gene_A, 11 gene_R, gene_R, circadian_clock circadian_clock evolve evolve 0-150000 0-150000 plot

plot A, A, RR AR 1 1 0.2 2 A R + 10 5 0.5 50 MA A 50 500 + MR A

0.01 + A A gene_A 1 50 A_gene_A 50 gene_R 1 A_gene_R 100 Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002 Circadian Clock object object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR rule rule circadian_clock circadian_clock {{ gene_A gene_A 50-> 50-> MA MA ++ gene_A gene_A A+gene_A 1->

A_gene_A A+gene_A 1-> A_gene_A A_gene_A A_gene_A 500-> 500-> MA MA ++ A_gene_A A_gene_A gene_R gene_R 0.01-> 0.01-> MR MR ++ gene_R gene_R A_gene_R A_gene_R 50-> 50-> MR MR ++ A_gene_R A_gene_R MA MA 50-> 50-> AA MR MR 5-> 5-> RR A+R A+R 2-> 2-> AR AR AR AR 1-> 1-> RR AA 1-> 1-> 0A 0A RR 0.2-> 0.2-> 0R 0R

MA 10-> 0MA MA 10-> 0MA MR MR 0.5-> 0.5-> 0MR 0MR A_gene_R 100-> A_gene_R 100-> A+gene_R A+gene_R A+gene_R 1-> A_gene_R A+gene_R 1-> A_gene_R A_gene_A A_gene_A 50-> 50-> A+gene_A A+gene_A }} system system 11 gene_A, gene_A, 11 gene_R, gene_R, circadian_clock circadian_clock evolve evolve 0-150000 0-150000 plot plot A, A, RR AR 1

1 0.2 2 A R + 10 5 0.5 50 MA A 50 500 + MR A 0.01 + A A gene_A

1 50 A_gene_A 50 gene_R 1 A_gene_R 100 Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002 Circadian Clock object object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR rule rule circadian_clock circadian_clock {{ gene_A gene_A 50-> 50-> MA MA ++ gene_A gene_A A+gene_A 1-> A_gene_A A+gene_A 1-> A_gene_A A_gene_A A_gene_A 500-> 500-> MA MA ++ A_gene_A

A_gene_A gene_R gene_R 0.01-> 0.01-> MR MR ++ gene_R gene_R A_gene_R A_gene_R 50-> 50-> MR MR ++ A_gene_R A_gene_R MA MA 50-> 50-> AA MR MR 5-> 5-> RR A+R A+R 2-> 2-> AR AR AR AR 1-> 1-> RR AA 1-> 1-> 0A 0A RR 0.2-> 0.2-> 0R 0R MA 10-> 0MA MA 10-> 0MA MR MR 0.5->

0.5-> 0MR 0MR A_gene_R 100-> A_gene_R 100-> A+gene_R A+gene_R A+gene_R 1-> A_gene_R A+gene_R 1-> A_gene_R A_gene_A A_gene_A 50-> 50-> A+gene_A A+gene_A }} system system 11 gene_A, gene_A, 11 gene_R, gene_R, circadian_clock circadian_clock evolve evolve 0-150000 0-150000 plot plot A, A, RR AR 1 1 0.2 2 A

R + 10 5 0.5 50 MA A 50 500 + MR A 0.01 + A A gene_A 1 50 A_gene_A

50 gene_R 1 A_gene_R 100 Vilar, Kueh, Barkai, Leibler, PNAS, 99, 9, 2002 Circadian Clock object object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR rule rule circadian_clock circadian_clock {{ gene_A gene_A 50-> 50-> MA MA ++ gene_A gene_A A+gene_A 1-> A_gene_A A+gene_A 1-> A_gene_A A_gene_A A_gene_A 500-> 500-> MA MA ++ A_gene_A A_gene_A gene_R gene_R 0.01-> 0.01-> MR MR ++ gene_R gene_R

A_gene_R A_gene_R 50-> 50-> MR MR ++ A_gene_R A_gene_R MA MA 50-> 50-> AA MR MR 5-> 5-> RR A+R A+R 2-> 2-> AR AR AR AR 1-> 1-> RR AA 1-> 1-> 0A 0A RR 0.2-> 0.2-> 0R 0R MA 10-> 0MA MA 10-> 0MA MR MR 0.5-> 0.5-> 0MR 0MR A_gene_R 100-> A_gene_R 100-> A+gene_R A+gene_R

A+gene_R 1-> A_gene_R A+gene_R 1-> A_gene_R A_gene_A A_gene_A 50-> 50-> A+gene_A A+gene_A }} system system 11 gene_A, gene_A, 11 gene_R, gene_R, circadian_clock circadian_clock evolve evolve 0-150000 0-150000 plot plot A, A, RR AR 1 1 0.2 2 A R + 10 5

0.5 50 MA A 50 500 + MR A 0.01 + A A gene_A 1 50 A_gene_A 50 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 object gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR gene_A,A_gene_A,gene_R,A_gene_R,MA,MR,A,R,AR rule rule circadian_clock circadian_clock {{ gene_A gene_A 50-> 50-> MA MA ++ gene_A gene_A A+gene_A 1-> A_gene_A A+gene_A 1-> A_gene_A A_gene_A A_gene_A 500-> 500-> MA MA ++ A_gene_A A_gene_A gene_R gene_R 0.01-> 0.01-> MR MR ++ gene_R gene_R A_gene_R A_gene_R 50-> 50-> MR MR ++ A_gene_R A_gene_R MA MA 50-> 50-> AA MR MR 5->

5-> RR A+R A+R 2-> 2-> AR AR AR AR 1-> 1-> RR AA 1-> 1-> 0A 0A RR 0.2-> 0.2-> 0R 0R MA 10-> 0MA MA 10-> 0MA MR MR 0.5-> 0.5-> 0MR 0MR knockout gene for R A_gene_R 100-> A+gene_R A_gene_R 100-> A+gene_R at step 50000 A+gene_R A+gene_R 1-> 1-> A_gene_R A_gene_R A_gene_A A_gene_A 50-> 50-> A+gene_A A+gene_A

}} system system 11 gene_A, gene_A, 11 gene_R, gene_R, -1 -1 [email protected] [email protected],, -1 -1 [email protected] [email protected],, circadian_clock circadian_clock evolve evolve 0-150000 0-150000 plot plot A, A, RR 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 AR 50 0 R 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'| a,u,v,x,a',u',v',x' V [ ] |v|x a [ ] |v'|x'a' Simulator attach rules: 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' a,u,v,x,a',u',v',x' V [ ] |v|x a [ a ] |v'|x' 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 Gabg 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 + || 4000 Gabg + |RL| 1.0e-5-> Ga, Gbg + |RL|

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|] 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. *M. Cavaliere,

Cavaliere, P. P. Frisco, Frisco, H. H. Hoogeboom, Hoogeboom, Computing by Only Observing, Lecture Notes in Computer Science Science 4036, 4036, Springer-Verlag. 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. *M. Cavaliere, Cavaliere, P. P. Frisco, Frisco, H.

H. Hoogeboom, Hoogeboom, Computing by Only Observing, Lecture Notes in Computer Science Science 4036, 4036, Springer-Verlag. 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 2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation.

Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

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    Considering a word's parts. Identify the word's root and any prefixes or suffixes. For example, "transport" has the root "port" which means "carry" and the prefix "trans" which means "across," so the word means "carrying across" or "carrying from one...
  • Ch. 10 Nutrition Created by Coach Luttrell Information

    Ch. 10 Nutrition Created by Coach Luttrell Information

    The six main categories of nutrients are: Carbohydrates. Proteins. Fats. Vitamins. Minerals. Water. Nutrients and Nutrition. Eating a variety of healthy foods will help you get the nutrients you need. Carbohydrates: sugars and starches that occur naturally in foods, mainly...
  • CONSTRUCTING A COIL POT in a FORM Waverly-Shell

    CONSTRUCTING A COIL POT in a FORM Waverly-Shell

    CONSTRUCTING A COIL POT in a FORM Waverly-Shell Rock Senior High CERAMICS 1 CONSTRUCTING A COIL POT OBJECTIVE: The student will learn how to use coil-building techniques to create a coil pot that incorporates variety and pattern within a cardboard...