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, Paris Diderot "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

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

Mutation and (Simple) Darwinian Selection

sequencesmaterials in excess

with

Error Thresholds

fraction of neutral mutants

superiority of master sequencesequence length

genotypic error threshold

phenotypic error threshold

Putting it All Together

selection

amplification

GUUGAGGUAG

GCAC

UCC GC C UGAC

UACCU A AC

CCUC

GCUGCUUC A AGUC

C UAGG

CAAU

UUGCGG

CCCUCUGACGGG

GUUGAGGUAGGCACUCCGCCUGACUACCUA......CCUAGGCAAUUUGCGGCCCUCUGACGGG

folding “representation” of phenotype by an equivalence class

error threshold(s)

Lecture Two.5…

2. (part 2) The Propagation of Genetic, Phenotypic, and Molecular information

TEE

Basics

T +

reaction velocity (flux) equilibrium constant

kinetic equilibrium

thermodynamic equilibrium

connects energetics with kinetics

Basics

R P

R

P

Reaction coordinate

Gib

bs fr

ee e

nerg

y

EEF ET

FE

TEE

Kinetic Proofreading Problem

andat steady-state

assume

discriminating factor

error rate

EEF ET

ET*EF*

FE

TEE

TE

FE

Kinetic Proofreading Scheme

drawing after Jeremy Owen

Energetic discrimination

wrong right

time

Kinetic discrimination

long time

short time

wrong right

time

long time

short time

Proofreading Schemes

S. Pigolotti & P. Sartori. J Stat Phys (2016) 162:1167–1182

Lecture Three

3. Modeling cellular information processing

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:

molecular species18 868 902 333 942 991 917 533 566 435 344 349

Signaling: A Circulatory System of Information

not a physical network, but a network of possibility

Start with simplicity…

Where To Begin ?

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

[A]

Kd = 0.1Kd = 0.5

Kd = 1

Kd = 10

Kd = 5

Kd = 2

[BA]Bt [BA]

Bt=

[A][A] + Kd

Bt = [B] + [BA]

B + Ak1��⇥���k�1

BA

Binding

B + Ak1��⇥���k�1

BA

Binding

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

� =[A]Kd

�

[BA]Bt

collapse all binding curves into one by using the dimensionless variable

[BA]Bt

=�

� + 1

[BA]Bt

=[A]

[A] + Kd

0 2 4 6 8 10 12 14 16 18 20

0

0.2

0.4

0.6

0.8

1

�(=[A]Kd

)

[BA]Bt

[A] = Kd

bt = 0.1

bt = 1

bt = 5

bt = 10

ator

[BA]Bt

=�

� + 1

bt =Bt

Kd

at =At

Kd

[BA]Bt

=2at

1 + at + bt +�

(1� at + bt)2 + 4at

blue: equilibrium solution in terms of known parameters

Ared: equilibrium solution in terms of free

B + Ak1��⇥���k�1

BA

Binding

v

vmax

quasi-steady state of ES

enzyme is saturated

k1, k�1 >> k2 quasi-equilibrium of ES

B + Ak1��⇥���k�1

BAk2�⇥ B + P

v

vmax=

�

� + 1

At � Bt

At � Km

� =[A]Km

v � dP

dt= k2[BA] = k2Bt

�

� + 1

with

when

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

substrate S

range of “first order kinetics” (linear regime)

range of “zero order kinetics”

range of “intermediary order kinetics”

�

[A] = Km =k�1 + k2

k1

At � Bt

Binding Equilibria As “Prefixes”

B + Ak1��⇥���k�1

BAk2�⇥ B + P

0 200 400 600 800 1000 12000

20

40

60

80

100

1042

1044

1046

1048

1051

0

BAA

_PP

Time [s]

num

ber o

f par

ticle

s

0 5 10 15 20 250

200

400

600

800

1000

BAA

P_P

num

ber o

f par

ticle

s

Time [s]

At � Bt At � Bt

Binding Equilibria As “Prefixes”

B

A

AA

A

a scaffold protein with n binding partners

k�1

k1

Multiple Binding Sites: Scaffolds

2n (+1)

n2n�1

molecular species

reactions

Combinatorial Reaction Network

23

n binding sites (disordered)

[BAn]Bt

=�

�

� + 1

⇥n

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

n=2

n=10

[BAn]Bt

�

n=1

for any finite � � 0 as n⇥⇤

⇤�

� + 1

⌅n

=1�

1 + 1�

⇥n � 0

Lost In (Combinatorial) Space

24

n binding sites (disordered)

[BAn]Bt

=�

�

� + 1

⇥n

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

n=2

n=10

[BAn]Bt

�

n=1

frac

tion o

f co

nfigura

tions ✓

n

j

◆/2n

Lost In (Combinatorial) Space

Sequential Binding

n=2

n=10

sequential binding all-or-none cooperativity (Hill)

[BAn]Bt

=�n(1� �)1� �n+1

[BAn]Bt

=�n

1 + �n

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

�

[BAn]Bt

�

n=2

n=10

n=1n=1

�n

1 + �n�⇥

n�⇥

�0 for � < 1,

1 for � > 1

a threshold for large n a step-function for large n

�n(1� �)1� �n+1

�⇤n�⇥

�0 for � ⇥ 1,

(�� 1)/� for � > 1

Sequential Binding & All-Or-None

C

B

C

A

BB

A

B C

B

C

A

B

B

A

B

C

B

C

A

BB

A

B

A

B

A

A

BB

v = k2Bt

��

1 + �

⇥2

v = k2Bt�

1 + �

⇥

1 + ⇥

v = k2Ct�⇥

1 + ⇥ + �⇥

v = k2Ct�⇥

1 + �⇥v = k2Bt⇥

1 + ⇥

�1� �

1 + �

⇥

k2k2

k2k2

or...

...

...

...

A � C

A �B

C ⇥ ¬A

or

sequential: first BC, then ABC

(this is non-competitive inhibition)

Binding Logic

A

B

A

B

A

A

BB

[BA2]Bt

=�

�

1 + �

⇥2

Increase total B. What happens?

The B Side

10 20 30 40 50

1

2

3

4

5

6

0

n=2

n=3

n=5

bt

[BAn]Kd

bt =12(1 + at) (@n = 2)

[BAn]Kd

= bt

�

⇤ 2at

1 + at + nbt +⇧

(1� at + nbt)2 + 4at

⇥

⌅n

The B Side

(e.g. a kinase)

(e.g a phosphatase)

A

B

T •T �

T •T �

A

B

T � T •

T = [T �] + [T •]

A + T � kA1��⇥���

kA�1

AT � kA2�⇥ A + T •

B + T • kB1��⇥���

kB�1

BT • kB2�⇥ B + T �

d[T •]dt

=kA2 At(Tt � [T •])

KAm + Tt � [T •]

� kB2 Bt[T •]

KBm + [T •]

A Do-Undo Loop

small G proteins

GDPRas GTPRas

Pi H2O

GEF

GAP

GTP GDP

guanine nucleotide exchange factor

GTPase-activating protein

heterotrimeric G proteins

G��GDPG↵��

GDPG↵

GTPG↵

RGSGTP

GDP

(a variety of combinations from 23 , 6 , 12 subunits)G↵ G� G�

regulator of G-protein signaling

active receptor

Loops EveryWhere

A

B

T � T •

tB =T

KBm

T = [T �] + [T •]d[T •]dt

=kA2 At(T � [T •])

KAm + T � [T •]

� kB2 Bt[T •]

KBm + [T •]

[T •]T

=2r

1 + r + (K � r)tB +�

(1 + r + (K � r)tB)2 � 4r(K � r)tB

r =kA2 at

kB2 bt

at =At

KAm

bt =Bt

KBm

K =KB

m

KAm

dimensionless

A Do-Undo Loop

with

with

r

(saturated regime)

steady-state solution of

(linear regime)

steady-state solution of[T •]T

d[T •]dt

=kA2 At

KAm

(T � [T •])� kB2 Bt

KBm

[T •]

d[T •]dt

⇥ kA2 At � kB

2 Bt

KAm = KB

m = 0.74 µM

[T •]T

=r

r + 1log10 tB

K =KB

m

KAm

= 1

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

with

n=2

n=10

sequential binding

[BAn]Bt

=�n(1� �)1� �n+1

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

�

n=1

�n(1� �)1� �n+1

�⇤n�⇥

�0 for � ⇥ 1,

(�� 1)/� for � > 1

A

B

r =kA2 at

kB2 bt

sequential phosphorylation w/ linear kinetics

T (0) T (1) T (2) T (3) T (4)

[T (n)]T

=rn(1� r)1� rn+1

The Do-Undo Loop Chain

and

...

the “input”

T •1

T �1

A � T •0

T �2

T1 = [T �1 ] + [T •

1 ]

B2

T •2 T2 = [T �

2 ] + [T •2 ]

Bn�1

Bn

T �n T •

n

T •n�1

T ⇥n�1

Tn = [T �n ] + [T •

n ]

Tn�1 = [T ⇥n�1] + [T •n�1]

the “output”

ri =kA

2 Ti�1

kB2 Bi

r1 =kA2 A

kB2 B

ri = r i = 2, . . . , n

the input variable

[T •n ]

Tn=

r1

r1 +r � 1rn � 1

rn�1(r � 1)rn � 1

B � B1

The Do-Undo Loop Cascade

⇥10�5

n=3 n=5

r r

[T •n ]

Tn=

r1

r1 +r � 1rn � 1

rn�1(r � 1)rn � 1

r1r1

[T •n ]

Tn

[T •n ]

Tn

notice the scale difference between n=3 and n=5

The Do-Undo Loop Cascade

1s10-8 1s10-7 1s10-6 1s10-5 1s10-40

0.2

0.4

0.6

0.8

1

111 112 121 211 222122

input

stea

dy-

stat

e re

adout

parameters from Huang/Ferrell

“122” cascade

37

The Do-Undo Loop Cascade With “Depth” and “Width”

A

B

T �T •

d[T •]dt

=kA2 At(T � [T •])

KAm + T � [T •]

+kT2 [T •](T � [T •])KT

m + T � [T •]� kB

2 Bt[T •]KB

m + [T •]

Eb = 0.1Ea = 40S = 200

K(a)m = 1100

K(s)m = 200

K(b)m = 11

k(a)2 = 0.1

k(b)2 = 10

k(s1)2 = 1

“on” state

“off” state

[T •]

Bt

0 1 2 3 4 5 60

50

100

150

200

The Do-Undo Loop With Feedback: Memory

lo hi

hi

lo

A

B

T �T •

[T •]

Bt

Double-Well Analogy

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

40