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")

• 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)

Schedule

#T. M. Murali

Assignments

1. Assignment 1, released on February 10, 2022, due by 11:59pm on February 17, 2022
2. Assignment 2, released on February 24, 2022, due by 11:59pm on March 18, 2022

Projects

Each student should give me their top three choices by 5pm on Monday March 14. I will create groups based on your choices. 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 methods section of the relevant paper or book chapter 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.

• 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".
• Fly central brain network: Webpage on this dataset (contains several useful links including the network and neuPrint API).
• Fly network among mechanosensory networks: Notebook.
• Comprehensive connectome of the mouse brain: Collected in a 2017 paper titled Organizing principles for the cerebral cortex network of commissural and association connections from findings in over 185 publications that appeared in the literature since 1974.
• Brain-wide mesoscale connectivity matrix in the mouse: Supplementary Table 2 in A mesoscale connectome of the mouse brain

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 central brain. 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.

There are over 100 algorithms developed for clustering graphs in order to find modules in them. The algorithms differ in several characteristics such as the definition of modules, the number of parameters used to define modules, whether modules can overlap or not, and the precise techniques used to compute them. This project will apply multiple such published algorithms to connectomes in order to discover how much the computed modules change based on the algorithm. The material in Chapter 9.3: Comparing and Aggregating Network Partitions of the textbook is relevant. I encourage the project group to read other papers on "consensus clustering" published in the literature, with my feedback and advice, of course. The steps in the project will include

• Decide a set of algorithms to compare after discussion with me.
• Download the code for each algorithm and making sure it runs well. If necessary, you may have to implement some algorithms, but I hope that work will be minimal.
• Develop and implement ideas and methods for comparing modules and partitions computed by different algorithms.
• Implement consensus clustering algorithms.
• Run these algorithms on connectomes and report your results.

Many techniques for determining connections among brain regions, e.g., diffusion tensor imaging or functional magnetic resonance imaging, result in undirected networks, i.e., we know that two regions \(a\) and \(b\) are connected by one or more nerves but we do not in which direction the connections go. This project will explore whether it is possible to analyze the edges and structure of an undirected network to predict the direction of each edge. The paper Inferring neural signalling directionality from undirected structural connectomes proposes methods to solve this problem. It defines use three methods: navigation efficiency, diffusion efficiency, and search information. The goal of the project will be to understand these methods, implement them, apply them to brain networks, and evaluate their effectiveness.

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.

What is an appropriate model of how the brain transmits information? Information transmission may be modeled as the passing of stochastic messages in parallel along the wiring of the human connectome. Under two natural assumptions, the paper Efficient coding in the economics of human brain connectomics proposes an approach based on shortest paths to measure the effective fidelity of a message passed between regions of the brain. Further, it uses a random walk-based idea to develop a notion of the rate of a message. This paper introduces a few new concepts in neuroscience that we have not discussed in class, so it will ideal for students who want to learn these concepts as part of a capstone project. Since this paper is long and detailed, this project will focus on the five hypotheses illustrated in Figure 1B. I will work with the students to define precisely which results in the paper should be replicated in this project.

We know that brain networks are modular, where each module is a sets 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?