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 Chapter 24

Chapter 15 2 Chapter 24 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.

Chapter 15 3 Chapter 24 Figure 24.1 Feedback and feedforward control loops that regulate heat shock in bacteria (modified from El-Samad, et al., 2006).

Chapter 15 4 Chapter 24 Figure 24.2 The gene regulatory circuit responsible for mammalian circadian rhythms.

Chapter 15 5 Chapter 24 Figure 24.3 The layers of feedback control in the Central Dogma (modified from (Alberts et al., 1998))

Chapter 15 6 Chapter 24 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.).

Chapter 15 7 Chapter 24 Process Control ConceptBiological Control Analog SensorConcentration of a protein SetpointImplicit: equilibrium concentration of protein ControllerTranscription factors Final control element Transcription apparatus; ribosomal machinery for protein translation ProcessCellular homeostasis Table 24.1 Analogies between process control concepts and gene transcription control concepts.

Chapter 15 8 Chapter 24 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

Chapter 15 9 Chapter 24 Drosophila Circadian Oscillator PER TIM PER TIM PER TIM DBT PER P P TIM P P DBT Cytoplasm Nucleus per tim

Chapter Chapter 24 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).

Chapter Chapter 24 Figure 24.6 Simulation of the circadian clock model.

Chapter Chapter 24 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)).

Chapter Chapter 24 Figure 24.8 Simulation of circadian clock model for entraining signal with period of 20 h.

Chapter Chapter 24 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

Chapter Chapter 24 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]

Chapter Chapter 24 Figure 24.9 Schematic of chemotaxis signaling pathway in E. coli (adapted from Rao et al., 2004).

Chapter Chapter 24 Figure Integral control feedback circuit representation of chemotaxis (adapted from Yi et al., 2000).

Chapter Chapter 24 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

Chapter Chapter 24 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

Chapter Chapter 24 Figure Simplified insulin signaling pathway for glucose uptake.

Chapter Chapter 24 Insulin-Stimulated GLUT4 Translocation Model

Chapter Chapter 24 Figure Schematic of 4 th order signal transduction cascade for Example 24.3, combined with first-order receptor activation (adapted from Heinrich et al., 2002).