Schedule

Introductory Videos

These videos provide introductions into the brain structure and function, and molecular and cell biology. I will play some of them in class.

• The Brain: Structure and Function (13:55")
• Cell theory (watch the first 1:40")
• Types of brain cells (19")
• Glial Cells, White Matter and Gray Matter (1:50")
• Neuron (11:20")
• Split brain experiments (a Flash-based game)
• Inside the Brain: Unraveling the Mystery of Alzheimer's Disease (4:22")
• Mechanisms and secrets of Alzheimer's disease: exploring the brain (6:26")

These videos discuss general molecular and cell biology.

• The Cell (7:21"): a general overview of cell structure from Nucleus Medical Media

• The DNA learning center has created several interesting videos.
  • Cell signals (I played this video in class)
  • The Central Dogma (several videos)
• The textbook "Biology" by Raven, Johnson, Losos, and Singer has several relevant videos:
  • Molecular biology of the gene
  • Cell communication
  • Gene regulation

Assignments

1. Assignment 1, released on February 11, 2020, due by 11:59pm on February 20, 2020
2. Assignment 2, released on February 27, 2020, due by 11:59pm on March 20, 2020

Projects

Each group should give me its top three choices by 5pm on Tuesday, February 25.

I have provided brief descriptions of a few project ideas below. I will develop the projects further and flesh out many details over the course of the meetings I will schedule with each group. I will make multiple connectomes available that can be used across different projects. There will be ample opportunity to add meat to each project, including ideas you develop yourself, visualizing networks in the cool ways we have seen in the textbook and in class, and displaying your results in interesting and compelling ways.

These guidelines will help you complete projects successfully.

• Read the relevant book chapter or the methods section of the relevant paper o carefully, in conjunction with the results and figures.
• Make a list of the functionality, steps, or data you will need to generate each panel of each figure.
• Create a detailed Google Doc with this information and share it with me.
• Remember that you do not have to implement every piece of analysis yourself. I allow you to use existing software packages.
• If you get overwhelmed, take it one panel at a time. If a panel looks very challenging, discuss it with me.
• Divide the tasks among the members of your group and set a timetable to follow.
• The more organized you are and the more you make regular progress each week, the greater your chances of success! Do not leave everything till the last couple of weeks.

• Fly hindbrain network: Webpage on this dataset (contains several useful links including the network and neuPrint API).
• Connectivity matrices (in .mat format) used in "A spectrum of routing strategies for brain networks".
• Networks used in "Navigable maps of structural brain networks across species".

In class, we have seen evidence that brain networks have the small-world property. Nodes in these networks have corresponded to macroscopic regions of the brain. Do networks at the neuronal level, i.e., where every node is a neuron, also have the small-world property? You will investigate this question in this project using the fly hindbrain dataset. The challenge is that this network contains 25,000 nodes, which means that you have to compute about 312 million pairs of shortest paths lengths. A major component of the project will be to devise sampling strategies that compute only a small fraction of all shortest paths yet still give high-quality estimates of the average shortest path length. A secondary component will be to do the same for the clustering coefficient as well.

In class, we have discussed algorithms for computing clusters/modules in connectomes. In this project, you will apply and test these algorithms on neuronal networks such as those for the fly hindbrain. Many of these algorithms are likely to run very slowly on large networks, so you have ample scope for developing clever strategies to speed them up. Another important direction will be to identify clusters (of neurons) that you compute with regions in the brain.

How are signals propagated efficiently in brain networks? Algorithms such as Dijkstra's require complete knowledge of all the nodes and edges in a graph. In the brain, a "node" is likely to have knowledge only of its "neighbours". How can we define an efficient routing protocol in this scenario? The authors of this paper use a simple decentralised protocol called "greedy routing" and demonstrate its efficacy in networks from several species.

The goal of this project is to implement this method and compare it to other shortest path algorithms, including Dijkstra's algorithm and the A* algorithm. Is the Bellman-Ford algorithm useful here? As part of the project, think about how to use it as an alternative to navigation routing. Develop methods to compare its performance to all the other algorithms. Replicate the results in Figures 2-4 and, if possible, Figure 5 in the paper.

This paper presents a family of biased random walks for routing in brain networks that combine local and global information. This approach is similar to shortest-path algorithms at one extreme and to diffusion based processes at the other.

In this project, you will implement the algorithm proposed in this paper and recreate the results in Figures 2, 3, and 5, and if possible, Figure 4.

We have seen in class that brain networks are modular, where each module is a set of node that is highly connected internally. How are intermodule connections distributed within a network? Rentian scaling is a concept in engineered circuit design. It states that the number of external connections between nodes in different modules is related to the number of nodes inside the modules by a power-law relationship. (Physical) Rentian scaling is a property of systems that are cost-efficiently embedded into physical space. It is what is called a "topo-physical" property because it combines information regarding the topological organization of the network with information about the physical placement of connections. In this project, you will compute the Rentian scaling of different brain networks. Two papers will be relevant here: Efficient Physical Embedding of Topologically Complex Information Processing Networks in Brains and Computer Circuits and Evidence of Rentian Scaling of Functional Modules in Diverse Biological Networks. Chapter 8.3.3: Rentian scaling of the textbook also covers this topic.

• There are different algorithms for computing modules. How much does the Rentian scaling property (the power in the law) vary depending on the algorithm?
• Does Rentian scaling change from one organism to another?
• There are two different notions of Rentian scale: topological and geometric. There are different ways to compute them. How do these values differ?

A 2017 paper titled Organizing principles for the cerebral cortex network of commissural and association connections has published and analyzed a comprehensive connectome of the mouse brain, collected from findings in over 185 publications that appeared in the literature since 1974. This project will analyze the structural properties of this connectome. If you are ambitious, you can try to correlate this network with the mouse connectome created independently by the Allen Institute for Brain Science.

In the class, we have studied and analysed several type of connectomes. Each of these connectomes arose from experimental observations of the brains of different organisms. We studied several types of properties of these connectomes. A fundamental question that arises now is what types of evolutionary processes in nature can generate the types of connectomes that exist in organisms. For example, the process is almost certainly not an Erdos-Renyi like model. This project will consider several mathematical models that have been proposed for connectomes and test these models for their ability to generate artificial networks with properties that match those of real connectomes such as the small world property and hierarchical modularity. The paper Resolving Structural Variability in Network Models and the Brain and Box 10.1: Growth Connectomics: Generative Models for Brain Networks in the textbook provide excellent starting points for this project. An important question to consider will be whether models should incorporate geometric constraints imposed by the structure of the brain.

Different individuals in the same species have connectomes that show remarkable architectural and wiring similarity. What is the reason? Could the connectivity patterns of neurons be encoded at the protein level? The paper A Genetic Model of the Connectome explores this idea through a hypothesis that the genetic identity of a neuron guides the formation of its synapses. Their specific hypothesis predicts the existence of subgraphs called bipartite cliques (bicliques) in the connectome.

An initial goal in this project is for you to read and understand the paper. After downloading the datasets, you will have to write software to recreate the results in Figures 2-4. To enumerate all maximal bicliques, you may use existing software packages.