23,24,25,26,29,30 giugno – 1 luglio 2009 - ore 10:00 -13:00
Regulation is a running theme throughout biology. At every level of organization, living systems use feedback control strategies to regulate their internal milieu in order to withstand the constant changes in their external environment. In this course we will develop the modeling and analysis tools necessary for exploring regulatory mechanisms in biology. We use these tools to study some examples of intricate biological control mechanisms at the molecular level and at the system level, showing how they achieve robustness and performance and drawing analogies with engineering control systems.
We will also highlight some of the unique challenges confronting biological control systems as they achieve function within the constraints of their distinct biochemical substrate. Among these, is the ever-present noise at the cellular level. A key source of this noise is the randomness that characterizes the motion of cellular constituents at the molecular level. Cellular noise not only results in random ?uctuations (overtime) within individual cells, but it is also a source of phenotypic variability among clonal cellular populations. Researchers are just now beginning to understand that the richness of stochastic phenomena in biology depends directly upon the interactions of dynamics and noise and upon the mechanisms through which these interactions occur.
We review a number of approaches for the analysis of stochastic fluctuation in gene expression. We will explore analytical and computational methods for the analysis of stochasticity in living cells, and demonstrate these techniques using examples of gene regulatory networks that suppress or exploit noise.
• Introduction to gene expression and gene regulatory networks.
• Deterministic vs. stochastic models.
• Mass-action kinetics. Michaelis-Menton kinetics. Reaction rate equations.
• Deterministic modeling at the system and cellular levels.
• Feedback and feedforward strategies. The heat-shock system.
• Biological oscillations. The cell-cycle.
• The stochastic chemical kinetics framework.
• A rigorous derivation of the chemical master equation. Moment computations.
Linear vs. nonlinear propensities.
• Linear noise approximations. Monte Carlo simulations.
• Gillespie’s Stochastic Simulation Algorithm. Variants of the SSA.
• Direct methods for the solution of the Chemical Master Equation. Finite State
Projections. Moment Closure methods.
• Intrinsic and extrinsic noise in gene expression. Propagation of noise in cell
networks. Noise suppression in cells. The role of feedback.
• How cells exploit noise. Noise focusing. Coherence resonance. Competence in B.
Subtilis. Bimodality and stochastic switches.
• The pap pili stochastic switch.
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