This course is an
introduction to dynamical systems, aimed at a quantitative understanding of the
biochemical kinetics that underlies cell biology. Background required is Chm 241 or equivalent basic physical
chemistry and basic mathematics through calculus. We will start with the dynamics of the simplest chemical
reactions: dimerization and the Michaelis-Menten enzyme mechanism. We will cover thermodynamic cycles and
regulation, multi-component and multi-time-scale kinetics through matrix and
eigenvalue methods; robustness and adaptation; limit cycles; stability; and
oscillating systems, such as those involved in the cell cycle and circadian
rhythms. We will cover the
dynamics coupled with spatial diffusion that leads to biological pattern
formation, and the small numbers problem - that cells often have only a few
copies of certain molecules, and therefore their fluctuations are large.
March 31
Introduction. What do we mean by complex systems? Elementary
kinetics. {KD/CV}
April 7 Dimensional analysis, time scales, model building, limit behavior. Examples: How Flipper Swims, simple kinetic models, steady-state assumptions, Shea-Ackers model of promoter states. {CV}
April 14 How sets of differential equations behave, Linear equations, eigenvalues, stability analysis, null clines, phase space. Examples: Genetic circuits, autoregulation, ultrasensitive switches.
{CV}
April 21
Regulation, control of energy flow. How binding alters the rates of biochemical cycles. Biological driving forces: ATP, and gradients
{KD}
April 28
Bifurcation analysis, bistability, continuation methods. Examples: cell-fate switch, lac operon, cross repression, positive feedback.
{CV}
May 5
Robustness and Adaptation. Bacterial chemotaxis. Homeostasis
{HL}
May 12 Robustness and Adaptation. Control theory, derivative and integral feedbacks {HL}
May 19
Oscillators. Damping. Ca2+, circadian rhythm, repressilator, cell cycle. {HL}
May 26
June 2 Stochasticity.
Fluctuations of molecule numbers in the cell. Gillespie algorithm. Single molecule experiments. Principle of Maximum Caliber.
{KD}