Neuro-Fuzzy-Chao-Criti-Plexity Scale-free Bio-systems · [SinI] (nM) Bistability Graded Switch Osc Pulse A R (protein/mRNA-s) k 3 (mRNA/s) 0A = 10,000 nM 0A = 10 nM Evolvability?

Neuro-Fuzzy-Chao-Criti-Plexityin

Scale-free Bio-systems

A HOT 50 years in Biological Design

Robust Yet Fragile Egos in Systems Biology

An autobiography

Design and Diversity in Cellular Networks

6

I'd like to share a revelation that I've had during my time here. It came to me when I tried to classify your species. I realized that you're not actually mammals. Every mammal on this planet instinctively develops a natural equilibrium with the surrounding environment, but you humans do not.

You move to an area, and you multiply, and multiply, until every natural resource is consumed. The only way you can survive is to spread to another area. There is another organism on this planet that follows the same pattern. A virus. Human beings are a disease, a cancer of this planet, you are a plague, and we are the cure.

Agent SmithThe Matrix

7

Everyone’s a virus

Environment

t

E1

E2

E3

E4

E2

E1

Organism 1 Organism 2

ω1ω1 ω2

ω2

pi

S1 S2

S3S4S5

SN

Sensors

pi

S1 S2

S3S4S5

SN

Outputsignals

quorumnoise

It’s a virus eat virus world out there.

8

Everyone’s a virus

It’s a virus eat virus world out there.

Evolution selects for strategies that win some environmental game played against nature and other organisms.

9

Immune cells

• They perform amazing engineering feats under the control of complex cellular networks

Onsum, Arkin, UCB Mione, Redd, UCLStossel

10

~1/50 of the known macrophage chemotaxis network

Fc- receptor c5a- receptor

Calcium control PIP3 control

Court

esy

of AfC

S

11

Everyone’s a virus

It’s a virus eat virus world out there.

Evolution selects for strategies that win some environmental game played against nature and other organisms.

Ultimately, we want to engineer biological systems that perform a designed function and NO MORE.

12

Niches are Dynamic

abiotoic reservoir

• Characteristic times may be spent in each environment.

• Environments themselves are variable.

13

Life Cycle

• Adaptability: Adjustment on the time scale of the life cycle of the organism

• Evolvability: Capacity for genetic changes to invade new life cycles

New niches with new lifecycles

Adaptability vs. Evolvability

14

• In a dynamic environment, the lineage that adapts first, wins

• Fewer mutations means faster evolution

• Are some biosystems constructed to minimize the mutations required to find improvements?

“Environment”

{ Parameter Space }

Pat

tern

{ Parameter Space }

Pat

tern

{ Parameter Space }

Pat

tern

{ Parameter Space }

Pat

tern“Environment”

• Modularity

• Robustness / Neutral drift improves functional sampling

• Shape of functionality in parameter space

• Minimize null regions in parameter space (entropy of multiple mutations)

Evolvability

Chris Voigt

15

Systems and Synthetic Biology• Systems biology seeks to uncover the design and

control principles of cellular systems through– Biophysical characterization of macromolecules and other cellular

structures– Comparative genomic analysis– Functional genomic and high-throughput phenotyping of cellular

systems– Mathematical modeling of regulatory networks and interacting cell

populations.

• Synthetic biology seeks to develop new designs in the biological substrate for biotechnological, medical, and material science.– Founded on the understanding garnered from systems biology– New modalities for genetic engineering and directed evolution– Scaling towards programmable biomaterials.

16

Systems biology is necessary

• Because of the highly interconnected nature of cellular networks

• Because it is the best way to understand what is controllable and what is not in pathway dynamics

• Because it discovers what designs evolution has arrived at to solve cellular engineering problems that we emulate in our own designs.

17

Synthetic biology

• There have been an number of impressive feats in design of cells that foreshadow a true revolution in rational cellular engineering!

• Our ability to manufacture new molecules and proteins with new and useful functional groups is rapidly outstripping our ability to predictively engineer new behavior into cells or control natural behavior.

• Cells are sensing, actuating, and evolving platforms for our engineering– our additions to them do not operate in isolation.

Design in Cellular Networks

19

Biological device physics

• Analog, asynchronous, nonlinear, and stochastic

• Evolution creates designs that make robust cellular function despite this

• Unlike in electronics, the theory for biomolecular devices is early at best and measurement technology is only beginning to mature.

20

SPICE Circuit Simulator• SPICE is a widely used circuit analysis package which allows the designer to

connect electronic devices into a circuit– and predicts the response of the circuit under specified conditions

• SPICE is a circuit simulator– it applies circuit analysis equations to the designed circuit to calculate currents and

voltages as a function of time– for any condition, it may require a lot of calculations to reach a final answer where all

the values are internally consistent

• But how does SPICE ‘know’ how a transistor behaves?

21

• Microelectronic manufacturing ‘fabs’ will measure thousands of devices in order to get accurate SPICE models

• A widely used SPICE model for transistors is BSIM 3.3

• The better the theoretical framework, the more generally applicable will be the results– and the model can be refined

22

Chemical Frequency Filtering

γ(1+sin(ωt)) A k

|A| = k(1 + ω2/k2)1/2|γ sin(ωt)|

0

0.02

0.04

0.06

0.08

0.1

0 0.2 0.4 0.6 0.8 1 1.2 1.4ω

Log(ω)

Title:Creator: Mathematica

P+γsin(ωt) A k1 k2

RB BC

First Order Reaction

Second Order Reaction

Equation for amplitudevery complicated

23

Positive feedback motifs

• FAK

• LAC

• Lambda

• HIV

Op Op lacZlacZ lacYlacY lacAlacA

II

YY

++

cIcI Op Op crocro+

-

LTRLTR tartar tattat

+

24

Bistability

A simple model of the positive feedback

Monostable

Weakly bistable

Irreversibly Bistable

kC=1.6kc

kc – catalytic constant for the trans-autophosphorylation.

Stat

iona

ry s

tate

[FA

K-I]

25

Single steady state

Two steady states

Oscillations

0 0.1 0.2 0.3 0.410-2

10-1

100

101

102

103

AR (protein/mRNA-s)

[Sin

I] (n

M)

Bistability

Osc PulseSwitchGraded

AR (protein/mRNA-s)

k 3(m

RN

A/s

)

0A = 10,000 nM

0A = 10 nM

Evolvability?

Chris Voigt

AR

k3

26

Enzymatic Futile Cycle w/ Noise

det

½=p1=p

0=p

0.3 0.5 1 1.5 2E+

0.005

0.01

0.05

0.1

0.5

1Xss

E0 E½ E1

1 2 3 4 5s�E+

-50

-40

-30

-20

-10

10SNR

tdBEfXKXkdt

XKXEk

XKXEkdXdX )(*

**

++

++

−

−−

+

++

++⎥

⎦

⎤⎢⎣

⎡+

−+

=−= σ

0)()()(

))(( 22

2

0

0 =+

+−+

+−− +

+

+++

−+

+−−+ Ef

XKKk

XXKXkXKXXEk

Essssss

ssss σ

pEEf ++ =)(

27

Noise induced Bistability

0 1 2 3 4 5 6 70

200

400

600

800

1000

1200

1400

1600

1800

2000

time,t

X,X

* ,E+ to

t

X X* E

tot

N

>< +E*X *X

>< +E

28

Noise

• One gene• Growing cell, 45 minutes division time• Average ~60 seconds between transcripts• Average 10 proteins/transcript:

• One gene• Growing cell, 45 minutes division time• Average ~60 seconds between transcripts• Average 10 proteins/transcript:

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40 45Time (minutes)

about50 molecules

25 molecules

Monte Carlo simulation data

Prom.Prom. aa

A A AA

29

Tat positive-feedback loop

• A standard engineering motif controls, in part, HIV gene expression.

• A positive feedback loop

LTRLTR tartar tattat

+

30

Viral Bistability+

gfpgfp IRESIRESLTRLTR tartar tattat 5’-LTR5’-LTR

0.1 1 10 100 1000FL1 LOG: GFP

Time

Fluoresence

31

Cells are collections of evolved functions

• Evolution has created a large repository of parts and capabilities who functions and interconnects we are just beginning to understand

• Discovery of new sequence and comparative analysis increasing the rate of confident hypothesis generation about these functions within limits.

• Biophysical characterization lags behind and lacks the “network effect” that sequence and even structure analysis currently enjoys.

Modules and Systems

33

Logic of B.subtilis stress response

• Network organization has a functional logic.• There are different levels of abstraction to be

found.

ComA~P

AbrB; SinR

DegU~P PhoP~PResD~P

Spo0A~P

AbrB

DegU~P ComK

AbrB; SinR;SigH

AbrBSinR

ComA~P

Sporulation

34

Consider Chemotaxis: E. coli

Periplasm

Cytoplasm

35

Consider Chemotaxis: E. coli

Periplasm

Cytoplasm

Sensor (Input

Transducer)Controller Actuator

Sensor (Output

Transducer)

output

error or actuating

signal

signal proportional

to inputinput

signal proportional

to output

(Adapted from Control Systems Engineering, N.S. Nise 2000)

receptors

CheAWYZ Flagella

cheB/cheR

Integral Feedback Controller

36

Organization of Phenotypes?

37

Clusters are functionally coherent

Receptors

Signal Transduction (che)

Hook and Flagellar Body

Flagellar export/Type III secretion

Flagellar length and motor control

Hypthothetical receptors

Cross-Regulation with Sporulation/Cell Cycle

38

Different modules for different livesAr

chea

lExt

rem

ophi

les

Spor

ulat

ors

Endo

path

ogen

sPl

ant p

atho

gens

Anim

al p

atho

gens

Endo

path

ogen

s

39

What Ontology Recovers Modules?

Color legend:

■ sensor

■ controller

■ actuator

■ cross-talk betweennetworks

■ unknown

Systems Ontology

40

Comparative analysis is especially important

These are the homologous chemotaxis pathways in E.coli and B. subtilis

They have the same wild-type behavior.Different biochemical mechanisms.

Different robustnesses! Chris Rao/John Kirby

Rao, CV, Kirby, J, Arkin, A,P. (2004) PLOS Biology, 2(2), 239-252

41

Differences in robustnessE . Coli B . subtilis

Do these differences lead to differences in actual fitness?

Do these differences lead to differences in actual fitness?

Chris Rao/John Kirby

Design of “Viruses”

Leor Weinberger, David Schaffer

43

BACKGROUND

• What is AIDS?• Actual clinical syndrome when immune system

breaks down• CD4+ T cell count < 200 cells µL & Opp. Infections

present

• How does HIV cause AIDS?• CD4+ T cell killing and eventual exhaustion of T

cell replenishment machinery (currently most accepted of 3 theors.)

• What is the treatment?• HAART (Highly Active Anti-Retroviral Therapy)

a.k.a. triple-drug cocktails reduce viral production and increase CD4 count.

• HAART decreases the rate of CD4+ cell turnover.• HAART delays progression to AIDS.

44

PROBLEMS WITH HAART• Serious side-effects

• Many patients can’t tolerate many of the 18 available drugs• Liver, Spleen, Pancreatic damage • Fat redistribution (humpback condition)

• Expensive• $15,000/year for drugs alone• Majority of 40 million infected live in 3rd world.

• Viral resistance• arises on average after 18 months of therapy

• Latent reservoirs of infection• resting cells not actively producing virus and thus not affected by

HAART• Estimates ⇒ more than 50-60 yrs. of continuous HAART to purge

latent reservoirs and eradicate HIV from patient.• Reactivation with IL-2, IL-7 did not work, prostratin is something

to hope for– but other things have worked in mice before.• Vaccines and other treatments not offering much hope

45

HIV-1 Disease Dynamics

Viral load during infection

Perelson & Nelson, SIAM Review, 41:3-44 (2000)

Clinical Latency

Viral set-point

46

• Identified reservoir is Memory CD4+ T cells having integrated proviral DNA• Population is small (few hundred cells/individual) and long-lived (lower limit

estimates ⇒ 80 yrs. of continuous HAART to purge latent reservoirs and eradicate HIV from patient.

•Reactivation (for e.g. with IL-2) does not work

Virus

Activated CD4(CCR5+)

Actively InfectedCD4

Memory CD4(CCR5lo)

Latently InfectedCD4

Stochastic non-expression

OriginallyProposed

Naive CD4(CCR5-)

Antigen

HIV-1 Post-integration (proviral) Latency

Antigen

47

Designing a therapy:Specifications

• Exploit HIV tendency to go latent• Easy to administer• Easy compliance• Easy to deliver (perhaps too easy)• Persistent• Surveillant: waits for HIV to begin to

express.

48

What’s the idea?

• Use a parasitic conditionally-replicating lentivirus

• Gut HIV-1 to create a harmless lentivirus– Lentiviruses seem not to be too bad in causing

problems simply due to integration.– Cells that have lentiviruses can express almost

unlimited virions if the cytotoxic viral proteins are removed

• Remove all capsid proteins to prevent our virus from being able to propagate by itself

• Add agents that allow it to both down-regulate HIV, yet steal the phage-coat made by HIV so our therapy can propagate.

49

How could we do it?

• Use the native Ψ packaging element to compete efficiently with HIV for it’s coat

• Use the woodchuck element, for example, to increase our viral RNA stability relative to HIV

• Express molecules to down-regulate HIV expression– Tat decoys– Competitors for Tar-binding– Targets for host-proteins necessary for HIV life-cycle– Combinations of these– (Currently implemented by siRNAs and a few other tricks)

• But will this work?– How much do we have to compete with HIV to steal the majority of phage coat– How much should we down regulate HIV for therapeutic effect

50

ProductivelyInfected Cells

(I) ActivatedCD4+ T lymphocytes

(T)HIV-1 Virus

Therapy Virus

Dually Infected Cells (ID)

Therapeutically Infected Cells (IT)

T

D

T d T k V T k V T

I k V T I

V n I c V D n I

λ

δ

δ δ

•

•

•

= − − −

= −

′= − + 2

T T T T

D T D

T D T

I k V T d I k V I

I k V I I

V P D n I c V

δ

δ

•

•

•

= − −

′= −

′= −

Expanded Clinical Model with crHIV-1 vector included

Down-regulation ofHIV-1 by crHIV-1 Competition for

Virion production

51

Steady state HIV-1 levels after crHIV-1 administration

52

Discussion1. The model gives a quantitative analysis of diverse gene

therapy approaches; the analysis is independent of the specific of anti-viral (down-regulating) gene used.

2. Use of multi-point and host-factor repression decreases mutational escape dramatically.

3. There does exist a parameter regime where a crHIV-1 therapeutic vector can persist along with HIV-1. A simple function R0T can be used to design crHIV-1 vectors that persist in vivo.

4. crHIV-1 can achieve a 3 log decrease in HIV-1 set point when packaging efficiency is 20 fold greater than HIV-1.

5. Not necessarily “better” to have a very efficient inhibitor of HIV-1 production.

53

Biological issues• Introduction of a new lentivirus into a human

host might cause pleiotropic disease (lymphoma,e.g.) (Unlikely)

• Uncontrolled mutation of HIV and therapy virus still leads to resistant virus (though less so)

• It is a stochastic non-linear control problem–we have little theory to help us.

• Introduction of new virus changes the viral ecosystem

54

Social Issues• Theoretically, our therapy virus is sexually

transmittable

• Epidemiological studies show that when medical treatments are introduced, promiscuity increases dramatically in many cases.

• The barrier to production of virus is relatively low

• Who will support or profit from a self-propagating persistent therapy?

• Is there anyway of assessing cost-benefit or risk when using engineered organisms such as this one?

55

Environment

t

E1

E2

E3

E4

E2

E1

Organism 1 Organism 2

ω1ω1 ω2

ω2

pi

S1 S2

S3S4S5

SN

Sensors

pi

S1 S2

S3S4S5

SNOutputsignals

quorum

noise

The game of life

56

Formal Model

xx

yy

sx1

E1gy>gx

E2gx>gy

p1,2

p2,1

1-p2,11-p1,2

Time-varying environment

a)

b)

Transition matrix TI,j(k)

Time k t Time (k+1) t

Ei?⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

)()()()(

2

2

1

1

kykxkykx

X k

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

++++

)1()1()1()1(

2

2

1

1

kykxkykx

no

EiObservers

Non-observers

yes

CorrectĒ

IncorrectĒ

pObs

1-pObs

Psii

Psij

Rate matrix Ri(k)

x1

x2

y1

y2 S2

S1sy1

sx2

sy2

sq1,2 sq2,1 sq1,2 sq2,1

Accuracy SiObservability pObs Mixing M

P1

P21-P2

1-P1

yy

xx

57

E1 E2

sx1

x ysy1

sx2

x ysy2

~n gen

~m gen

e.g. x=pili; y=no piliE1=in host; E2=out

IF E1: selects for x, against yE2: selects against x, for y

E1 E2 E1 E2

x

y

Example: two environments, two moves, no sensor

Denise Wolf, Vijay Vazirani

58

1.ALL cells in state x

2.ALL cells in state y

3.Statically mixed population (some x, some y)

4.Phase variation of individual cells between x and y

y

E1 E2

x

x y

With no sensor, the options are…Denise Wolf, Vijay Vazirani

59

1.ALL cells in state x

2.ALL cells in state y

3.Statically mixed population (some x, some y)

4.Phase variation of individual cells between x and y

Extinction

E1 E2 E1 ..

With no sensor, the options are…

y

E1 E2

x

x y

Denise Wolf, Vijay Vazirani

60

1.ALL cells in state x

2.ALL cells in state y

3.Statically mixed population (some x, some y)

4.Phase variation of individual cells between x and y

Extinction

E1 E2 E1 ..

With no sensor, the options are…

y

E1 E2

x

x y

Denise Wolf, Vijay Vazirani

61

1.ALL cells in state x

2.ALL cells in state y

3.Statically mixed population (some x, some y)

4.Phase variation of individual cells between x and y

Extinction

With no sensor, the options are…

y

E1 E2

x

x y

Denise Wolf, Vijay Vazirani

62

1.ALL cells in state x

2.ALL cells in state y

3.Statically mixed population (some x, some y)

4.Phase variation of individual cells between x and y

Proliferation!

With no sensor, the options are…

y

E1 E2

x

x y

Denise Wolf, Vijay Vazirani

63

This is a Devil’s compromise: Phase-variation behavior is not optimal in any one environment but necessary for survival with noisy sensors in a fluctuatingenvironment.

Rate of X Y Switching

Rate

of Y

X Sw

itch

ing

Phase variation for survival

Denise Wolf, Vijay Vazirani

64

Learning Environment from Cell State

O=High prob. observable transitions;A=Moderate accuracy.N=High additive noise.

SensorBased Pure;LPF

Temporally or spatially varying environment with each environmental state selecting for a single cell state.

O=High prob. observable transitions;A=High accuracy; or moderate accuracy and low noise N.

SensorBasedPure

O=High prob. observable transitions;A=Poor accuracy.N=High additive noise.

SensorBasedMixed;LPF

•Devil’s Compromise lifecycle.

•Asymmetric lifecycle required.

•Optimal mixing probabilities biased toward selected cell-states in dominant environmental states.

O=High prob. observable transitions;A=Poor accuracy

SensorBasedMixed

Frequency dependent growth curves with mixed ESS. Perfect sensors

D=Long delays relative to env. transition times.

O=Low prob. observable transitions over DC or extinction set.

•Devil’s Compromise (DC) lifecycle: time varying environment with different environmental states selecting for different cell states. •Optimal switching rates a function of lifecycle asymmetries and environmental autocorrelation.•Time variation required (spatial variation insufficient).

No sensorsRandomPhaseVariation(RPV)

Environmental profileSensor profileStrategy

Denise Wolf, Vijay Vazirani

Div

ersi

ty S

trat

egie

s

65

Robustness and Fragility

• The stratagems of a cell evolve in a given environment for robust survival.

• Evolution writes an internal model of the environment into the genome.

• But the system is fragile both – to certain changes in the environment (though there

are evolvable designs)– And certain random changes in its process structure.

• It’s not clear if cells are more or less robust than, say, this laptop.

66

Engineering beyond the bioreactor

• Engineering organisms for use outside the controlled production of biochemicals or to instrument them with a few fluorescent proteins requires a better understanding of the cellular system and its evolution.

– Engineering microbes for drug production– Engineering microbes for bioremediation– Engineering microbes for killing tumors– Engineering viruses for gene therapy– Engineering mosquitoes for malarial control– Engineering corn for agriculture

• Can we turn use a similar approach to engineering biological circuits as we do to engineering electronic circuits?

67

Productivity Trends

68

Exponentially More, Exponentially Cheaper Data

• Already large amounts of data, but incomplete

• Exponential increase: faster than Moore’s law

• Key is translation of data into knowledge with tools that enable human understanding and help direct experimentation

• And GOOD theory of design and synthesis of biological networks!

Plot due to Rob Carlson

Ron Weiss

69

Acknowledgements

Jay Keasling, BerkeleyDavid Schaffer, BerkeleyHenry Bourne, UCSF

Funding

NIGMS, NIHITO, DARPAOBER, DOE

Games and StressAmoolya Singh

Denise WolfChris Voigt

ChemotaxisChris Rao

MotifsMichael Samoilov

Chris Voigt

HIVLeor Weinberger

Arkin Group Collaborators

Happy Birthday, John!