1 Dynamics and Control of Biological Systems Chapter 24 addresses a variety of analysis problems in the field of biosystems: Systems Biology Gene Regulation.

1

Dynamics and Control of Biological Systems

Chapter 24 addresses a variety of analysis problems in the field of biosystems:

• Systems Biology• Gene Regulation

• Circadian Rhythm Clock Network• Signal Transduction Networks

• Chemotaxis• Insulin Mediated Glucose Uptake• Simple Phosphorylation Transduction Cascade

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What is “Systems Biology”?[WTEC Benchmark Study (2005): M. Cassman, A. Arkin, F. Doyle, F. Katagiri, D. Lauffenburger, C. Stokes]

[also: Nature, Dec 22, 2005]

Primary Definition: The understanding of biological network behavior through the application of modeling and simulation, tightly linked to experiment

Related Ideas– Identification and validation of networks– Creation of appropriate datasets– Development of tools for data acquisition and software

Motivation: Phenotype is governed by the behavior of networks, rather than the operation of single genes. Understanding the dynamics of even the simplest biological networks requires the application of modeling and simulation.

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Folding Process

Synthesis of Heat Shock Proteins

(FtsH and DnaK)

DNAKBinding to s32

s32

SynthesisHEAT

Folded Proteins32++

Figure 24.1 Feedback and feedforward control loops that regulate heat shock in bacteria (modified from El-Samad, et

al., 2006).

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Transcription

LIGHT

PERTranslation

Phosphorylation & Dimerization of PER, CRY

cryTranscription

CRYTranslation

Nucleus

CytoplasmCell Membrane

Figure 24.2 The gene regulatory circuit responsible for mammalian circadian rhythms.

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Transcription

Nucleus

Cytoplasm

Cell Membrane

Nuclear Transport

Translation ProteinActivation

primarytranscript mRNA protein

activeprotein

Figure 24.3 The layers of feedback control in the Central Dogma (modified from (Alberts et al., 1998))

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G1

Autoregulation

TF1

Multi-Component Loop

G1

TF1

TF2

G2G1TF1

FeedforwardLoop

TF2

G2

G1

SIMO Module

TF1

MIMO Module

G1TF1

Regulator Chain

TF2 G2 TF3 G3

G2 G3 G1 G2 G3

TF1 TF2

Figure 24.4 Examples of circuit motifs in yeast (adapted from (Lee et al., 2002)). The rectangles denote promoter regions on a

gene (G1, G2, etc.) and the circles are transcription factors (TF1, TF2, etc.).

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Process Control Concept Biological Control Analog

Sensor Concentration of a protein

Setpoint Implicit: equilibrium concentration of protein

Controller Transcription factors

Final control element Transcription apparatus; ribosomal

machinery for protein translation

Process Cellular homeostasis

Table 24.1 Analogies between process control concepts and gene transcription control concepts.

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Circadian Rhythms

Circadian rhythms = self-sustained biological rhythms characterized by a free-running period of about 24h (circa diem)

Circadian rhythms characteristics:• General – bacteria, fungi, plants, flies, fish, mice, humans, etc.• Entrainment by light-dark cycles (zeitgeber)• Phase shifting by light pulses• Temperature compensation

Circadian rhythms occur at the molecular level

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Drosophila Circadian Oscillator

PER

TIM

PERTIM

PERTIM

DBT

PERP

P

TIMP

P

DBT

Cytoplasm

Nucleus

pertim

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perTranscription

LIGHT

PERTranslation

Phosphorylation & Dimerization of PER, TIM

timTranscription

TIMTranslation

Nucleus

CytoplasmCell Membrane

TIMDegradation

TranscriptionProcess

LIGHT

Protein (P)Translation and

DegradationProcesses

mRNA(M)

Figure 24.5 Schematic of negative feedback control of Drosophila circadian clock (adapted from (Tyson et al., 1999)):

detailed system (top), and simplified model (bottom).

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0 20 40 60 80 1000

1

2

3

mR

NA

Time (h)

0 20 40 60 80 1000

1

2

3

4

Pro

tein

Time (h)

Figure 24.6 Simulation of the circadian clock model.

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0 20 40 60 80 1000

1

2

3

4

mR

NA

Time (h)

0 20 40 60 80 1000

2

4

6P

rote

in

Time (h)

Figure 24.7 Simulation of circadian clock model for varying values of m (1.0 (solid), 1.1 (dashed), 1.5 (dash-dot), 2.0

(dotted), 4.0 (asterisk)).

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0 50 100 150 200 250 300 350 4000

2

4

mR

NA

Time (h)

0 50 100 150 200 250 300 350 4000

5

Pro

tein

Time (h)

0 50 100 150 200 250 300 350 400

100

200

Ke

q

Time (h)

Figure 24.8 Simulation of circadian clock model for entraining signal with period of 20 h.

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Implications from Systems Biology Studies

• Robustness characteristics of feedback architecture under stochastic uncertainty

• Underlying design principles

• Nature of entrainment, and systems characterization

• Possible therapeutic ramifications (mutants, etc.)

• General biological oscillator insights

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Bacterial Chemotaxis

Process by which motile bacteria sense chemical gradients and move in favorable directions

E. coli alternates between:– Smooth runs (flagella spin counterclockwise)

– Tumble (flagella spin clockwise)

Random walk that is biased towards chemical gradient

Impossible to detect gradient across length of body

Key property: perfect adaptation– Steady-state tumbling frequency in uniform environment is independent of

environment concentration level

[wikipedia]

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Cell Membrane

LIGAND

Motor(tumble)

Yphosphorylation

Ydephosphorylation

CheW-CheAmethylation

CheW-CheAdemethylationCheR

CheZ

CheYp

CheY

Bphosphorylation

Bdephosphorylation

CheBp

CheB

Figure 24.9 Schematic of chemotaxis signaling pathway in E. coli (adapted from Rao et al., 2004).

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Ky

-x

y0

u ++++

-1s

Figure 24.10 Integral control feedback circuit representation of chemotaxis (adapted from Yi et al., 2000).

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Insights Gained from Systems Biology Approach

• Study reveals that robustness facilitates analysis (specific parameters not required, module can be isolated)

• Robustness properties point to reliable performance over environmental perturbations or mutations – suggesting preference for evolution

• Rao et al. study points to limitations in homologous gene analysis

• Narrowly tuned ranges are often key for homeostasis, and integral control can help attain such performance

• Integral control leads to robustness in biochemical networks

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Type 2 Diabetes Mellitus

A metabolic disorder primarily characterized by hyperglycemia and insulin resistance

US: 14 million with associated annual medical costs of $132 billion

Worldwide: 350 million by the year 2030

Linked to obesity due to high caloric intake combined with low physical activity – progresses through insulin resistance

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Cell Membrane

INSULIN

Insulin ReceptorDynamics

CheZ

RECEPTOR

Signal Transduction

Cascade

GlucoseTransporter

Biomechanics

GLUT4

Figure 24.11 Simplified insulin signaling pathway for glucose uptake.

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Insulin-Stimulated GLUT4 Translocation Model

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Figure 24.12 Schematic of 4th order signal transduction cascade for Example 24.3, combined with first-order receptor

activation (adapted from Heinrich et al., 2002).