Nov 8: Eric Deeds, University of California at Los Angeles "The evolution of cellular individuality" Nov 15: Daniel Merkle, University of Southern Denmark "Graph rewriting and chemistry"

Nov 22: Jean Krivine, IRIF, Université de Paris "From molecules to systems: the problem of knowledge representation in molecular biology" Nov 29: Eric Smith, Earth Life Sciences Institute, Tokyo “Easy and Hard in the Origin of Life" Dec 6: Massimiliano Esposito, University of Luxembourg "Thermodynamics of Open Chemical Reaction Networks: Theory and Applications"

Dec 13: Yarden Katz, Harvard Medical School "Cells as cognitive creatures" Jan 17: Aleksandra Walczak, ENS Paris "Prediction in immune repertoires"

Jan 24: Tommy Kirchhausen, Harvard Medical School "Imaging sub-cellular dynamics from molecules to multicellular organisms"

1. The Topology of the Possible (La représentation de l’information biologique)

Previous Lectures And Look-Ahead

2. Propagation of Genetic, Phenotypic, and Molecular information (Limites de la transmission de l’information biologique)

3. Modeling cellular information processing the classical way (Modélisation ‘classique’ du traitement de l’information cellulaire)

4. Modeling cellular information processing the rule-based way (Modélisation basé sur les règles; introduction)

5. Examples of rule-based models (Modélisation basé sur les règles; examples)

6. Causality in rule-based dynamics (Causalité)

7. Combinatorial scaffolding (Echafaudage combinatoire)

8. Cellular learning? (Apprentissage cellulaire?)

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

substrate S1

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1

0 500 1000 1500 2000 25000

5

10

15

20

25

30

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 1 2 3 4 5 60

50

100

150

200

3

N

D

N/D

AA/N

bB

Cc

e E

n

d

f F

C/F

E/F

D

2

3 a bistable switch

a homeostat

2

32

22

spatially interrupted

“homeostat”

Delta / Notch: Loops All The Way Down

r

saturated regimesteady-state solution in

linear regimesteady-state solution in

[T •]T

KAm = KB

m = 0.74 µM

log10 tB

K =KB

m

KAm

= 1

The Do-Undo Loop: An “Atom” Of Molecular Control

A

B

T � T •

assuming

0 0.5 1 1.5 2K( ) / P( )

0

0.2

0.4

0.6

0.8

1

S(x~

p?) /

S( )

at s

tead

y-sta

te

smart : S=20,000 / K+P = 1000 / Kd = 250, Km = 354dumb : S=20,000 / K+P = 1000 / Kd = 250, Km = 354by equation (14)by equation (18)by equation (13)

Details Matter

Pablo Picasso: Don Quixote (1955)

...maps, not the territory

...about converting facts into knowledge

...never right or wrong, only useful or useless

Models Are…

Lecture Four

4. Modeling cellular information processing with rules (Kappa)

Kinase

Phosphatase

Transcription Factor

Caspase

Receptor

Enzyme

pro-apoptotic

pro-survival

GAP/GEF

GTPase

G-protein

Acetylase

Deacetylase

Ribosomal subunit

Direct Stimulatory Modification

Direct Inhibitory ModificationMultistep Stimulatory Modification Multistep Inhibitory ModificationTentative Stimulatory Modification

Tentative Inhibitory ModificationSeparation of Subunits or Cleavage Products Joining of Subunits

Translocation Transcriptional Stimulatory Modification Transcriptional Inhibitory Modification

CELL SIGNALING TECHNOLOGY www.cellsignal.com

Pathway Diagram Keys

IP3R

IntracellularCa2+ Store

Ca2+

CREBMEF2C

p38

p38 JNK1/2

MKK3/4/6 MKK4/7

Lyn

Akt

PTEN

SHIP

Akt

FoxO

mTORGSK-3

IκBNFAT

p70S6K

LynSyk

Btk

SHP-2

PLCγ2

GabShc

GRB2

GR

B2

BLN

K

PKC

JNK Erk1/2

Erk1/2

MEK1/2

c-Raf

Ras

NF-κB

NF-κBIκB

IKK

PKC

CaMK

ATF-2 Jun Egr-1 Elk-1 Bcl-xL Bfl-1 NFAT

CD19

CD19

CD19

CD45

CaM

Bam32

CIN85

MEKKs

SOS

RasGAP

RasGRP

Bcl-6 Oct-2 Ets-1

CD40

LAB

LAB

CblCsk

Cbp/PAG

SHP-1BCAP

CARMA1

Ag

CD22 FcγRIIB1

FcγRIIB1

Bcl10

RhoA

Rap

Rac/cdc42

Rac

RapLRiam

Cofilin

Pyk2

HS1

Dok-1

Dok-3

CD19

PIR-B

Ezrin

Bam32

clathrin

TAK1

Calcineurin

CR

AC

Cha

nnel

Ora

i1

Ca2+

STIM1

SHP-2SHP-1

MALT1

GRB2 Vav

BCR

p85PI3Kp110

ProteasomalDegradation

ProteinSynthesis

Transcription

Growth Arrest,Apoptosis

DAGCa2+

Ca2+

PIP3

Transcription

mIgα/β α/β mIg

PI(4,5)P2

CytoskeletalRearrangements and

Integrin Activation

DAG

DAG

PIP3

IP3

LipidRaft

AggregationBCR

Internalization

Glucose Uptake

Glycolysis

ATPGeneration

Nucleus

Cytoplasm

B Cell Receptor Signaling

© 2002 – 2014 Cell Signaling Technology, Inc.

© Cell-Signaling Technology

Signaling: A Circulatory System of Information

cell fate, division, repair,

cell death, motility,

morphology, …

tasks:

Signaling: A Circulatory System of Information

not a physical network, but a network of possibility

d

dtx1 = x5 + x9 + x4 + x3 + x7 + x8 + x2 + x6 � x1x13 � x1x13 � x1x12 � x1x11

d

dtx2 = x3 � x2

d

dtx3 = x1x11 � x3 � x3

d

dtx4 = x5 � x4

d

dtx5 = x1x13 � x5 � x5

d

dtx6 = x7 � x6

d

dtx7 = x1x12 � x7 � x7

d

dtx8 = x9 � x8

d

dtx9 = x1x13 � x9 � x9

d

dtx10 = x2 + x6

d

dtx11 = x3 + x8 � x1x11

d

dtx12 = x4 + x7 � x1x12

d

dtx13 = x5 + x9 � x1x13 � x1x13

K Sa

b

x1 = [K]x2 = [KaSab]x3 = [KaSb]x4 = [KaSa]x5 = [KaS]x6 = [KbSab]x7 = [KbSa]x8 = [KbSb]x9 = [KbS]

x10 = [Sab]x11 = [Sb]x12 = [Sa]x13 = [S]

Extensional Models

13 equations

K Sa

b

Extensional Models

kinase-related terms

+ 21 new equations

K Sa

bP

phosphatase-related terms

adding a phosphatase

13 equations, each changed !

Extensional Models

kinase-related terms

the formalism of differential equations does not represent agents, only their concentration

the formalism of differential equations entangles kinetics and causation

the formalism of differential equations separates model and knowledge

• need to know in advance all molecular species that can occur • vulnerable to combinatorial explosions • cumbersome to build and modify large models

• physical time is inadequate for describing distributed systems • hard to reason about “mechanisms of action”

• “I forgot why I put this term in my model...” • models are not self-documenting and don’t organize knowledge effectively

Limitations of the ODE Framework

precedes modelingunderstanding

Modeling in Physics (Approximately)

Jørn Utzon, 1958

Models

Jørn Utzon, 1958

Models

A model should be a formal and executable representation of the facts it rests upon.

Modeling in Biology ?

precedesmodeling understanding

Laura Nevola and Ernest Giralt, Chem. Commun., 2015, 51, 3302-3315

The Scope: Proteins as “Agents”

M. Battles, V. Más, E. Olmedillas, O. Cano, M. Vázquez, L. Rodríguez, J. Melero, & J. McLellan. “Structure and immunogenicity of pre-fusion-stabilized human metapneumovirus F glycoprotein,” Nat Commun 8, 1528 (2017)

The Scope: Proteins as “Agents”

21

The Same Protein In a Different State

22

ethane ethanol

NOT The Same Molecule In a Different State

Abstraction Level

As

rp

Cuv

agent (protein) of type A

site “s” of “A”

state (“phosphorylated”) of site “s” of “A”

bond between site “p” of “A” and site “u” of “C”

complex of “A” and “C”

A( s{p}[.], r{p}[.], p[1] ), C( v[.],u[1] )

Graphs And Site Graphs

B D

EA

C

B D

EA

C

site graph (contact graph)plain graph

B

D

EA

DB

site graph (pattern)

A B C

r

s

uv

w

x

y

zu

uv

w

wy

x

up

u

p

z

NN-

N N

H2N

O NH2

O

NH2

NH2O

O

O

O

H

H2N

O

NH

O

PO

O

-OO

N

N

HO H

H

NH2

H

H

OH

Co+

C

O

C

H

H HH

Chemical Abstraction For Comparison

chemistry

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NO

C

H

H2C

H2CCH2

CH2

CH2

ON C

H

H2C

H2C CH2

CH2

CH2

NO

C

H

C

ON C

H

C

mat

ch

rewrite

before after

Graph Rewriting

As

rB

x

As

rpB

x y

zCuv

mat

ch

before after

rewrite

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As

rp Bx y

zC

uv

As

rB

x

As

rp

Cuv

implementation: Mød implementation: Kappa

“molecular biology”

O−

N+

O−

N+

N+ O−

λρ

O

O

O

O

O

OCC

C

N N

O O

e

C

C

C

ON

KL R

H D G

l r

m k n

DPO Graph Rewriting in Chemistry

C

O

CH

H3

.. ..

H

C

O

CH

H3

..H

O

CH

H

..

..CH3

O

CH

H.. ..

CH2

CH

CH3 C

CHO

H

..

..

O

H..

H2

H

C C

CHO

H

..

..

H2

O....

CH3 H

protonation

enolization (i)

attack at carbocation

deprotonation

CO

H

C

O

C

CO

H

C

O

C

Unboxing of Rules

C

O

CH

H3

.. ..

H

C

O

CH

H3

..H

O

CH

H

..

..CH3

O

CH

H.. ..

CH2

CH

CH3 C

CHO

H

..

..

O

H..

H2

H

C C

CHO

H

..

..

H2

O....

CH3 H

protonation

enolization (i)

attack at carbocation

deprotonation

not exposed

“Axin binds a region in the armadillo repeat of -catenin, if -catenin is un-phosphorylated at T41 and S29.”

ctnnb1arm1arm2

S29S33

S37

T41

arm3dest

agent abstraction

AxinRGS

CBD

DIXaDIXb

i_PP

i_CK1 i_GSK

an interaction rule

Axin ctnnb1arm1S29

T41

CBD Axin ctnnb1arm1S29

T41

CBD

Fusing Modeling and Knowledge Representation

t=0

t=20

t=40 t=60

dynamic evolution

Statics and Dynamics

01

23

static expansion

dynamic evolution

Dynamics

choose initial “soup” of molecules

identify all its matchings in the soup; for each rule

compute its probability to fire, based on the # of matchings

determine the time of the next eventchoose a rule and a matching according to probability

apply the rule to the matched molecules

rule A s Bs A s Bs

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The Rate Constant

r2

r1

A

r1

B

M�1s�1

mol�1s�1

molecule�1s�1� =k

A V

� =k

V

k

�volume

time molecule

⇥

volume V in which the reaction occurs

The Stochastic Rate Constant

volume swept by collision cross-section by 1 A

opportunities for that A to hit some B

opportunities for some A to hit some B

rate per time and volume

probability of encountering a B

The Stochastic Rate Constant

M�1s�1

A

s

d

B

s

Ad

s

B

sp p

A

s

d

B

sp

12

3

213

The Mixture

rule activity

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A

s

d

B

s

Ad

s

B

s

pp

A

s

d

B

sp

rule A s Bs A s Bsrule r

A

s

d

B

s

Ad

s

B

sp p

A

s

d

B

sp

1 2 3

213

an embedding of

Lr<latexit sha1_base64="KCBVXWmrjCnXjK408LkHDWxs6iY=">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</latexit>

Rr<latexit sha1_base64="vLAxWoOeAgBmqcHkzxtRjD1+KaU=">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</latexit>

Lr<latexit sha1_base64="KCBVXWmrjCnXjK408LkHDWxs6iY=">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</latexit>

(will modify…)

Rule Application

... probability density of catching a fish in the time intervala · d� [�, � + d� ]

t t + dt

P0(t + �t) = P0(t)(1� a�t)

t = 0

p(t)dt =?

dinner!

no dinner up to time t

dinner within time t

probability density of dinner at time t

Memoryless Process

P0(t) = e�at

P (t) = 1� e�at

vR = k[A][B]R : A + Bk�⇥ something

p(t) = �e��t

nAnB

p(t) = � e��t

for an individual reaction event

� = ⇥nAnB

� =k

A Vwith molecule�1s�1

that many possible events

for the reaction with

The “First” Event In A Reaction Channel

n reaction types with activitiesGiven:

CTMC

(1) probability that reaction i happens at time t and it is the first:

with

Want to know: probability that the first reaction happens at time t and it is reaction i

(2)

rule activities

rules

system activity

advance time

select rule

update

initialize

r : Lr → Rr @ γr<latexit sha1_base64="YytpGP/Db2mVcD45Pb6iYEeqhzo=">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</latexit>

λ<latexit sha1_base64="45D28HOpz1dvBLei+CETTig2xoU=">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</latexit>

αr<latexit sha1_base64="5Rl2vAkBiIKWq7B+v6fxjs587wI=">AAACx3icbVHLattAFB2rj6TuK2mX3QwVhi4SIYXSZhkwlJZ2kUKcGCxjrkZX0ZAZzTAzMnaFFv2Fbtsf6Cf1bzq2RamdXBg4nDPnPjMtuHVx/KcX3Lv/4OHe/qP+4ydPnz0/OHxxaVVtGI6YEsqMM7AoeIUjx53AsTYIMhN4ld0MV/rVHI3lqrpwS41TCdcVLzgD56lxCkKXMDOzgzCO4nXQ2yDpQEi6OJ8d9n6nuWK1xMoxAdZOkli7aQPGcSaw7Q/S2qIGdgPXOPGwAol22qw7bunAMzktlPGvcnTN9u9yHOVzrm1nXmzc//1rQFq7lJnPKMGVtr+jrci7tEntitNpwytdO6zYpqGiFtQpuloTzblB5sTSA2CG+6EoK8EAc36ZW1UWS+lwoW07oMMSpT+ZWVJe0S9wgWN6TEFYRf+N+xm0hiiKtlKwje+IldK6Y59qS7X8GxrMmWdzLNJhmDTpqtIHZWQTJm3Hu7XgW3E7cuuPm+ye8ja4PImSOEq+vg3P3nVn3ievyGvyhiTkPTkjH8k5GRFGBPlBfpJfwadABfNgsfka9DrPS7IVwfe/Revf+Q==</latexit>

all and

Basic CTMC Loop

AssembleRead Execute

Explain

Cohere

Models as “Executable Knowledge”

AssembleRead Execute

papers ODEs

Structured staging area

for

Knowledge aggregation

Kappa rules

debugger

data repositories

reachables (s)

invariants (s)

fragments (s)

traces (d)

Explain

DIN (d)

stories (d)

Cohere

Kappa model

influence map (s)

observables (d)

contact map (s)

Models as “Executable Knowledge”

kappalanguage.org

(includes a detailed language manual)

AzA z Az A z

#1L #2L #2R#1R

L R

2 1 12

AzA z8 9

s sp u

AzA z8 9

s sup

M

2

M2

AzA z AzA z

#1L #2L #1R #2R

L R

1 2 1 2

AzA z8 9

s sp u

AzA z8 9

s sup

M M1

1

AzA z AzA z

#1L #2L #1R #2R

s s s suu pu

L R

1 2 1 2

AzA z AzA z8 9 8 9

s suu

s su p

M M1

1

AzA z Az A z

#1L #2L #2R#1R

s s ssuu p u

L R

2 1 12

AzA z AzA z8 9 8 9

s suu

s sp u

M

2

M2

Rule Symmetry

Case A

Case B

indistinguishable microstates; two embeddings represent the same physical event

distinguishable microstates; two embeddings represent different physical events

A z

x

BByy

AzA z

xx

By

A z

x

A z

x

BByy

AzA z

xx

III III

231

647 5

1198 10 12

number of distinct classes of connected components

Symmetry

number of isomorphic instances

in component c

number of symmetries of component c

total symmetries in pattern

Your Options?

rule

activity

(1) deterministic view

(2) nondeterministic view

(3) “mathematical” view

AyA xA x Ay

A xy

A xy

Ax

y

A yx

A xy

A xy

Ax

y

A yx

A xyA xy

Ax

y

A yx

b u

u

b

Molecular Ambiguity