The courses will start from introductory level and get to the state of the art. Each course will start with a 2 h lecture and end with 1h of “problem class” (e.g. journal club or hands-on computational class). Students are required to organize and work in groups prior to the problem class, according to the assignment announced during the lectures. There are six slots of group-work time, which is one per course.
In the first lecture we will introduce the basic concepts of decision-making theory and Reinforcement Learning and discuss how they can help us in understanding the principles that underlie effective search strategies. In the interactive class, we will discuss the biological applications to search by living organisms.
Recognition of pathogens relies on the diversity of immune receptor proteins. Recent experiments that sequence the entire immune cell repertoires provide a new opportunity for quantitative insight into naturally occurring diversity and how it is generated. I will show how applying statistical inference to recent experiments that sequence entire immune repertoires we can quantify diversity of this functional ensemble and sharing of repertoires between individuals. I will discuss how using the characterized repertoires of healthy individuals as a baseline we can identify statistical outliers that respond to viruses or are present in people with identified conditions. I will also present theoretical approaches to thinking about immune repertoires that minimize harm from infections.
Our knowledge of biological mechanisms has been derived from the intensive study of a just a handful of genetically amenable model organisms. Thus, a fair amount is known about conserved fundamental processes, such as cell division and secretion, but comparatively little about the myriad adaptations that promoted radiation in less well-studied branches of the tree of life. A focus on adaptation can reveal fundamental principles of biological organisation and mechanisms of evolution, while also creating opportunities to identify new problems or approach long-standing problems from new directions. Understudied groups are increasingly amenable to investigation due to advances in DNA synthesis, genome sequencing, mass spectrometry and bioinformatics. I will discuss the diverse topics of cytoplasmic streaming through fungal cellular networks, the evolution of multicellular complexity, and organelle diversification, and show how in each case quantitative methods played a key role to enable discovery and deepen understanding.
Phytoplankton moving in the ocean, spermatozoa making their way through the female reproductive tract and bacteria that swim through pores within soil or sediment interact with a surrounding fluid. Their length scales are small enough so that viscous effects dominate inertial effects. We will describe a methodology that can be used to capture the coupled system of an elastic actuated object and a viscous, incompressible fluid. We will explore a few case studies of biological systems and discuss how modeling choices were made and what was learned from the computational simulations. In addition, participants will have a chance to experiment with this methodology in a hands-on computational session.
Some 15 years ago, colleagues from the Cystic Fibrosis and Pulmonary Biology Institute at UNC came over to our applied mathematics group to help them try to understand mucus transport in a novel “lungs in a dish” cell culture. The Director of the Institute, Ric Boucher, wanted us to appreciate that “mucus is hot” at the time, and it has not cooled off yet. In this talk, I will tell the story of what we’ve learned since that initial conversation, and how our interwoven experimental-theoretical progress is now integrated into clinical practice
In several collaborations with molecular biologists and pharmaco-engineers, the role of molecular anchors that crosslink larger species is essential. One cannot directly observe the binding and unbinding of the anchors; rather one observes the mobility of the effector species without versus with the presence of molecular anchors. In mucus, antibodies are the anchors, while mucin polymers and pathogens (viruses or bacteria) are the effectors. In the nuclei of eukaryote cells, genes within chromosomal DNA are the effectors while “structural maintenance of chromosome” proteins, e.g., condensin and cohesin, are the anchors. In cellular cytoplasm, molecular proteins dynein and kinesin are anchors while microtubules and cargo are the effectors. In these and other biological contexts, weak and short-lived binding of many anchors leads to much greater functionality than tight binding kinetics! Furthermore, the functionalities are wildly diverse, underscoring the flexibility of the paradigm: immobilization of pathogens, self-organized gene communities for nuclear catalysis, and rapid transport of cellular cargo across the cell. Another emerging instance involves small cytoplasmic proteins that crosslink distinct complexes which then phase separate, creating membrane-less cellular compartments.
In our collaborations with experimentalists, we define success in terms of our ability to discern among competing underlying mechanisms from experimental data, to construct mechanistic models, to robustly infer model parameters from the experimental data, and then to computationally reproduce the experimental observations. The extent to which experiment and computation agree provides a happiness metric for our collaboration. In this interactive session, we will present the experimental data, our model selection methods, numerical codes for the mechanistic models, and then model parameters that yield poor versus weak reproduction of experimental data. One of the biological systems described in the first two lectures will be used to illustrate a happy collaboration