Complex Biological Systems, 2015

The q-bio summer school on Complex Biological Systems

What makes biology different from the inanimate world is what’s increasingly referred to as ‘complexity’. Complexity means many things, but for us it will mean that biological organisms are characterized by hierarchies of self-assembled networks. These are networks of interacting molecules at the level of the cell, interacting molecules and cells at the level of tissues, interacting organs at the level of the organisms and finally interacting organisms at the level of eco-systems. These interactions are enormous in number, are organized in space and time and are typically non-linear, making the task of understanding them in full generality currently impossible. However what we can do is to understand fundamental properties of simpler interacting non-linear systems, and use that to help us figure out specific questions about cellular, organismal or eco-system responses. For example, bacterial and mammalian cells undergo chemotaxis. But chemotaxis involves some rudimentary information processing, and a cellular “decision”. How do biological networks process information and how does that information processing lead to a cellular decision is the kind of question that we ask.

In the first part of the course, we will look at small systems and try to understand the consequences of nonlinearity. What we’ll find is that nonlinear biochemical networks display fascinating and non-trivial behavior that has important biological consequences. We will explore some of these consequences, at different scales. We will also look at some exciting engineering applications in the field of synthetic biology.

In the second part of the course, we will ask how we can use biological data to figure out the structure and properties of biological networks. and give an introduction to some modern methods of data analysis. In the process we’ll also encounter fascinating discussions on whether biological systems are robust, what robustness means, whether evolution is an optimizer, etc. Biological case studies will include examination of the lac operon, lysis-lysogeny in phage infected bacteria, competence in B. subtillis, chemotaxis, differentiation of stem cells, the MAP kinase cascade in mammalian cells, circadian oscillations in biology and several seminal papers in synthetic biology, cancer modeling and immune system modeling.

The course organizers are Ashok Prasad[1], Patrick Shipman[2]. We are really excited to be organizing this school. Please address all questions to an organizer.

Course Outline

Dynamical Systems: Linear systems of differential equations; Non-linear differential equations; one-dimensional flows; bifurcations and fixed points; higher-dimensional flows; limit cycles; chaos.

Biological Applications: Network motifs and their properties; switches and oscillators; circadian rhythms; synchronization of oscillations.

Analysis of Data: Takens Theorem.