BME 230A: Computational Genomics Overview

Course Information

• Course Title: Introduction to Computational Genomics and Systems Biology
• Instructor: Vanessa D Jonsson
• University: University of California, Santa Cruz
• Course: BME 230A
• Semester: Winter 2025

Instructors

• Vanessa Jonsson
• Benedict Paten
• Josh Stuart

Teaching Assistants

• Lydia Mok (Jonsson)
• Gabriel Penunuri (Paten/Stuart)

Class Overview

• Models and methods for single cell RNA seq analysis (5 weeks)
• Efficient sequence comparison (2.5 weeks)
• Somatic Genomics (1 week)
• Intro to AI in biology (1.5 weeks)

Course Policies and Logistics

• Lectures: Tuesdays and Thursdays, 3:20-4:55 pm, PhysSciences 110
• Lectures will be posted on Canvas
• 3 problem sets, posted and submitted on Canvas
• Jupyter notebooks posted and submitted on Canvas
• Collaboration allowed on all homework except midterm and final
• Students must record collaborators and contributions
• Questions and homework discussions on Discord
• Some problems will involve rudimentary programming using Google Colab or Jupyter notebooks

Grading Rubric

• 15% Project proposal presentation (3 slides/ 3 mins per presentation): background/problem/proposed work.
• 25% In-class Jupyter notebooks (submitted at end of lecture day)
• 10% Homework 1: (Jonsson/Mok theoretical + practice, due Jan 21)
• 10% Homework 2: (Jonsson/Mok theoretical + practice, due Feb 11)
• 10% Homework 3: (Paten, due Feb 11)
• 30% Final Project (written report 15%, oral presentation 15%)

Models and Methods in Single Cell RNA Seq

• Introduction
• Dimensionality Reduction/Clustering
• Modeling Counts (statistical distributions)
• Generalized Linear Models
• Variance Stabilization
• Differential Testing
• Multiple Testing, Part 1
• Multiple Testing, Part 2
• Biophysical Models, Part 1 (Subject to change)
• Biophysical Models, Part 2 (Subject to change)

Acknowledgements

• Several slides sourced from and inspired by "An Elementary Introduction to Computational Biology of single-cell RNA-seq." by Lior Pachter, California Institute of Technology.

Learning Objectives

• Understand the scope of the class
• Topics covered in the first 5 weeks
• Understand gene expression matrices
• Matrices as linear maps
• Data/Simpson's paradox
• Purpose of single-cell RNA seq
• Single-cell RNA-seq experimental and analytical pipeline

What the Course is About

• Computational biology: Study of models and methods used in biology and for interpreting biological data
• Warnings:
  • Much jargon (underlined for emphasis).
  • Outcomes depend on prior knowledge of prerequisites.
  • Course focused on one specific area for pedagogical clarity.

Be Careful with Jargon

• Computational biology draws on multiple disciplines (biology, bioengineering, CS, EE, math, stats).
• Terminology can vary, possibly confusing.

(Ideal) Prerequisites

• Mathematics (single/multivariate calculus, linear algebra, measure theory, discrete math.)
• Probability and statistics (probability theory, applied stats, theoretical stats)
• Computer science (programming, algorithms, data structures, software engineering)
• Biology (molecular/cell biology, immunology, neuroscience, evolution, biophysics)
• Domain-specific biological knowledge

Focus for the Single Cell Course

• Focus on common ideas and concepts across many applications.
• Focus on single-cell RNA seq (Lecture 2 will provide more detail).
• Primary focus on the gene expression matrix.
• Background material will be referenced at the end of each slide deck

Single-cell RNA-seq

• Single-cell RNA-seq is not single, cell, or RNA (Lecture 2)
• Single-cell RNA-seq: Group of constantly improving technologies/analysis tools
  • Input: Cells
  • Output: Gene expression matrix (proxy)

What is a Gene Expression Matrix?

• Expression: Process where information in a gene is used to generate protein/non-coding RNA
• Gene: Term coined by Johannsen (1857-1927), evolving meaning since 1909
• Matrix: Rectangular array of numbers for representing linear maps

The Meaning of "Gene Expression"

• Central Dogma: Information cannot exit a protein
• Sequence of amino acids carries information
• Directionality of information: DNA to RNA to Protein

Watson's Confusion

• Diagram showing DNA replication, transcription and translation is a reaction network rather than central dogma

A Reaction Network of Biopolymers

• Mathematical model of interactions between biopolymers like DNA, RNA and Protein with differential equations

Deciphering the "Genetic Code"

• 1953: DNA double helix discovery
• 1954: RNA Tie Club
• 1955: Adaptor hypothesis suggested
• 1956: Exploring nucleotide requirements for amino acids coding

4^2 < 20 < 4^3

• Theory on amino-acid order in nucleic acid strand
• 20 naturally occurring amino acids versus 4 nucleotides

A Sense and Nonsense Proposal

• Mechanism for coding frame determination (using “comma-free code”)
• Specific assignment of nucleotide triplets for "sense" and "nonsense" codons needed

Two Simple Observations, a Question, and a Theorem

• Repeats and shifts of sense triplets are nonsense.
• Question: Maximum size of a triplet comma-free code for a 4-letter alphabet?
• Theorem: Maximum size is 20.

The Genetic Code

• Determined through experimental series
• Key contributors: Grunberg-Manago, Holley, Khorana, Nirenberg, and Singer

The Genetic Code (Amino Acid Table)

• Amino acid 3-letter codes and single-letter codes

There's Plenty of Room at the Bottom

• Richard Feynman's 1959 Caltech lecture on potential of manipulating matter on atomic/molecular scale
• Importance of having tools developed to get “to the bottom” of gene expression

What is a Gene?

• Gene expression influenced by epigenetic modifications and regulatory networks
• Single gene can produce multiple RNA/protein isoforms through alternative splicing
• Non-coding genes can also produce molecules

Why a Gene Expression Matrix?

• A rectangular array is sufficient to represent a set of variables

A Matrix is Code for a (Linear) Function

• Matrix represents function, mapping input vectors to output vectors

How a Matrix Describes (is code for) a Function

• Matrix multiplication as a function

The Rank of a Matrix

• Rank: Dimension of the image (result of the transformation).

Singular Value Decomposition

• Decomposing a matrix into a product of three matrices: U, Σ, and V*
• U, V are orthogonal matrices, Σ is a diagonal matrix

Recall PCA BME 205

• Principal Component Analysis, used to find patterns in multivariate datasets through Singular Value Decomposition

Principal Component Analysis Can Be Derived by SVD

• Finding eigenvectors/eigenvalues of the covariance matrix is linked to SVD
• Data matrix decomposition via SVD produces principal components

Application to Dimension Reduction

• Using SVD to reduce dimensionality of datasets

A (Statistics) Convention for Tables

• Matrices in statistics represent observations (rows) and features (columns)
• Regression models described as linear combinations of explanatory variables (Xβ + є)

Confusion between the Mathematics and Statistics Conventions

• Seurat and Scanpy: Different conventions for rows/columns in data tables

Summary

• Expression: Process where gene information creates RNA/protein products
• Gene: Term coined by Johannsen, meaning slightly altered over the years
• Matrix: Rectangular array for representing a linear map.
• Gene expression matrix is more than a table, not immediately about expression, without context, may yield uncertain interpretation.

Why Single-Cell RNA-seq?

• Bulk RNA-seq averaging is problematic; single-cell is needed to resolve biases
• Simpson's paradox in bulk data analysis reveals averaging problems
• Resolution increases, introduce more uncertainty

Getting to the Bottom

• Lack of resolution in gene/cell expression masks important relationships/factors
• In this context, getting to the bottom means having proper cell and isoform resolution

The Purpose of Single-Cell RNA-seq

• Decompose tissue/organ expression into its constituent parts.
• Differentiate cell types with molecular signatures.
• Determine cellular differentiation trajectories.
• Develop biomarkers for disease

Overview of a Single-Cell RNA-Seq Experiment and Analysis

• Full workflow diagram of experiment preparation and analysis steps.
• Includes variance stabilization, normalization, SVD, linear regression, dimensionality reduction, etc.

Single-cell RNA-seq as a Theme for Computational Biology

• Data analysis in single-cell RNA-seq utilizes advanced data structures and algorithms pertinent to genomics.
• Statistical challenges are common in biological sciences.
• Mathematical models of biological mechanisms are critical.
• Methods frequently used in three different computational biology apps.
• Large, readily available single-cell dataset.

Single-cell RNA-seq as a Theme: Limitations

• Computational biology has vast unexplored areas.
• Single-cell RNA-seq is primarily count data; other aspects are not covered
• This course is only a survey; a vast number of topics are skipped.

Discord

• Use Discord platform for general questions, student-to-student and instructor-student discussion.

Additional References

• Provide examples of Simpson's paradox in computational biology.
• Link to relevant resources, like Strang's video lectures on linear algebra.

This quiz covers the key concepts and methods discussed in the BME 230A course, including single cell RNA sequencing, sequence comparison, and somatic genomics. Assess your understanding of AI applications in biology as well. Prepare to test your comprehension of the introductory materials and course logistics.