APh 161: Dynamics of Transcriptional Regulation

This page contains my lecture outline and notes for a set of lectures that I will be giving in [1], Rob Phillips's course on Physical Biology of the Cell. This page is mainly intended as a place for me to keep my notes, but might be useful as a reference for the lecture (the final lecture notes will be posted on the APh 161 web page).

Goals

• Motivate the role of dynamics and feedack in the physical biology of the cell
• Provide mathematical tools for analyzing the dynamics of transcriptional regulation in the cell
• Work through some case studies that serve as model systems for feedback control in cells

Lecture 1: Feedback and Dynamics in Cells

This lecture will be a powerpoint-style lecture that tries to motivate the role of dynamics and feedback in cells and describes how we can analyze models to obtain insights into the dynamics. We focus on the lac operon as the main object of study.

Lecture Outline How cells regulate function Motivating example #1: lac operon Going from cartoons → numbers: rates and transfer curves The fole of dynamics: stability, performance, robustness Methods of modeling: chemical kinetics, statistical mechanics, Hill functions Worked example: dynamical model for lac

Lecture Materials Lecture slides MATLAB code Reading Ch 19 of the course text J. M. G. Vilar, C. C. Guet and S. Leibler, "Modeling network dynamics: the lac operon, a case study. Journal of Cell Biology, 161:471-476, 2003. N. Yildirim, M. Santillan, D. Horike and M. C. Mackey, "Dynamics and bistability in a reduced model of the lac operon". Chaos, 14(2):279-292, 2004.

Notes

• I'll mainly be using materials from others for the overview parts of this lecture. I hope to get some of Christina Smolke's very nice slides from the CSHL "Engineering Principles in Biological Systems" meeting in Dec 2006, plus use things from Rob's slides from previous years.
• I need to figure out a good way of going from the equilibrium stat mech analysis to the dynamics using Hill functions, etc. The main issue is figure out how to rigorously transition to the rate and to find some data that support the approach.
• The mini-review paper by Vilar, Guet and Leibler provides a good summary of some of the approaches and limitations of modeling, using lac. It doesn't go into much detail, so mainly useful as a broad overview paper.
• The paper by Yildirim et al takes a fairly detailed model of the lac operon that was developed by Yildirim and Mackey (Biophysical Journal, 2003) and simplifies it to get a three dimensional model that they claim captures the main features of interest. They make use dynamical systems concepts (bistability, parameteric stability diagrams, bifurcations) to study the system. They compare their results to data and explore its predictive abilities.

Tutorial Interlude: Dynamical Systems 101

Tutorial Outline Modeling using ODEs (question → model) Dynamic behavior and stability Example #1: lac revisited (pictures) Analysis tools in MATLAB Example #2: represillator

Tutorial Materials Tutorial slides MATLAB code Additional Information CDS 101/110 lectures on dynamic behavior Chapter 4 of Åström and Murray

Notes

• This material will come from CDS 101/110, Week 3 - Dynamic Behavior. Pretty much the only change is going to be to swap out the examples with ones from biology (mainly lac and repressilator).
• I'll focus a fair bit on the use of MATLAB as a tool in this tutorial and stay away from doing things by hand. My feeling is that you want to be good at both - sketching things out in the sand and using tools like MATLAB to increase understanding (and do the "dirty" parts like making sure the curves have just the right shape, etc).

Lecture 2: Case Studies and Calculations

Lecture Outline Genetic switch in $\lambda$ Questions that we want to ask Modeling of the represillator Analysis and answers to questions/predictions Represillator Questions that we want to ask Modeling of the represillator Analysis and answers to questions/predictions Recap: the big piciture

Lecture Materials Lecture slides MATLAB code Reading Chapter 19 of course text

Notes

• The first part of this lecture will be a "stick in the sand" style lecture - working out everything by hand, on the board. The follows the material in Chapter 19 of the text.