Dynamics and Control
of Biological Systems
Chapter 24
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
1
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]
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Chapter24
Chapter
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.
2
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Chapter24
Chapter
s32
Synthesis
+
+
s32
Synthesis of Heat
Shock Proteins
(FtsH and DnaK)
HEAT
Folding
Process
Folded Protein
DNAK
Binding to s32
Figure 24.1 Feedback and feedforward control loops that
regulate heat shock in bacteria (modified from El-Samad, et al.,
2006).
3
Phosphorylation &
Dimerization of PER, CRY
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Chapter24
Chapter
PER
Translation
CRY
Translation
per
Transcription
cry
Transcription
LIGHT
Nucleus
Cytoplasm
Cell Membrane
Figure 24.2 The gene regulatory circuit responsible for
mammalian circadian rhythms.
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Chapter24
Chapter
Transcription
primary
transcript
Nuclear
Transport
mRNA
Translation
protein
Protein
Activation
active
protein
Nucleus
Cytoplasm
Cell Membrane
Figure 24.3 The layers of feedback control in the Central
Dogma (modified from (Alberts et al., 1998))
5
Multi-Component
Loop
Autoregulation
Feedforward
Loop
G2
G1
TF1
TF1
TF1
TF2
G1
TF2
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Chapter24
Chapter
G1
SIMO Module
MIMO Module
TF1
G1
G2
G2
TF1
G3
TF2
G1
G2
G3
Regulator Chain
TF1
G1
TF2
G2
TF3
G3
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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Chapter24
Chapter
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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Chapter24
Chapter
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
8
Drosophila Circadian Oscillator
PER
DBT
P
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Chapter24
Chapter
PER
P
PER
TIM
P
PER
TIM
TIM
P
per
tim
Nucleus
DBT
TIM
Cytoplasm
9
LIGHT
Phosphorylation &
Dimerization of PER, TIM
TIM
Degradation
PER
Translation
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Chapter24
Chapter
TIM
Translation
per
Transcription
tim
Transcription
Nucleus
Cytoplasm
Cell Membrane
LIGHT
Transcription
Process
mRNA(M)
Translation and
Degradation
Processes
Protein (P)
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).
10
2
1
0
0
20
40
60
80
100
80
100
Time (h)
4
Protein
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Chapter24
Chapter
mRNA
3
3
2
1
0
0
20
40
60
Time (h)
Figure 24.6 Simulation of the circadian clock model.
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mRNA
4
3
2
1
0
20
40
60
80
100
80
100
Time (h)
6
Protein
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Chapter24
Chapter
0
4
2
0
0
20
40
60
Time (h)
Figure 24.7 Simulation of circadian clock model for varying
values of nm (1.0 (solid), 1.1 (dashed), 1.5 (dash-dot), 2.0
(dotted), 4.0 (asterisk)).
12
mRNA
4
2
0
0
50
100
150
200
250
300
350
400
250
300
350
400
250
300
350
400
Protein
5
0
0
50
100
150
200
Time (h)
Keq
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Time (h)
200
100
0
50
100
150
200
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)
[wikipedia]
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
15
LIGAND
CheW-CheA
CheW-CheA
methylation
demethylation
CheR
15
Chapter24
Chapter
Y
dephosphorylation
CheZ
B
CheY
dephosphorylation
CheB
Y
phosphorylation
B
phosphorylation
CheYp
CheBp
Cell Membrane
Motor
(tumble)
Figure 24.9 Schematic of chemotaxis signaling pathway in E.
coli (adapted from Rao et al., 2004).
16
y0
15
Chapter24
Chapter
u
K
+
+
-x
+
+
y
-1
s
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
19
INSULIN
RECEPTOR
15
Chapter24
Chapter
Insulin
Receptor
Dynamics
Signal
Transduction
Cascade
CheZ
Glucose
Transporter
Biomechanics
Cell Membrane
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).
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