Fourth q-bio Summer School: Stochastic Biochemistry

In this theme, we will explore stochasticity in the modeling of biochemical systems. In particular, we will concentrate on the effects that small numbers of important molecules (i.e. genes, RNAs and proteins) have on the dynamics of living cells. We will review experimental manifestations of stochastic effects in molecular biology, as can be measured using single cell and single molecule techniques. We will discuss the most recent analytical and numerical methods that are used to model these systems and show how these methods can improve interpretation of experimental data. We will study how different cellular mechanisms control and/or exploit randomness in order to survive in uncertain environments. Similarly, we will explore how single-cell measurements of cell-to-cell variability can reveal more information about underlying cellular mechanisms.

This section of the summer school will include a number of instructor-suggested group projects, in which students will apply various numerical techniques to formulate, identify and solve stochastic models for gene regulatory systems. Students will then apply these tools to model experimental flow cytometry or other single-cell data. Access and knowledge of Matlab will be helpful, but is not strictly necessary.

This section of the summer school is organized by Brian Munsky. Please address all questions about this section of the summer school to its organizer.

Lecturers Include

• Babetta Marrone, Los Alamos National Lab
• Brian Munsky, Los Alamos National Lab
• Ilya Nemenman, Emory University
• Arjun Raj, University of Pennsylvania
• Christopher Voigt, University of California, San Francisco
• Jim Werner, Los Alamos National Lab
• Anton Zilman, Los Alamos National Lab

Topics Include

• Introduction to Stochasticity. The importance of stochasticity in gene regulatory networks. Key examples from the literature.
• Discussion of the importance of stochasticity in small populations. Stochastic Phenomena: switching, focusing, resonance, filtering.
• The effects of positive and negative feedback.
• The physics behind stochastic chemical kinetics.
• Connection between deterministic and stochastic reaction rates.
• Derivation of the Master Equation for discrete stochastic processes.
• Solving the Chemical Master Equation: exact solutions for linear propensity functions,
• Kinetic Monte Carlo algorithms: Tau Leaping. Chemical Langevin equation. Time separation schemes. Hybrid methods.
• Density Computation Approaches: Finite State projections techniques, Moment Generating Function Techniques, Moment Closure Techniques, Fokker Planck equation.
• Simplification of complex biochemical processes.
• Switch rate analyses, waiting/completion times.
• Single cell measurement techniques: flow cytometry, fluorescence microscopy, time lapse microscopy.
• Using fluctuations to infer system mechanisms and parameters.
• History of Stochastic Modeling in Physics.
• Signal Processing in Biochemical networks.
• Synthetic Biology