### 23 Jan 2020 » A Bayesian phylogenetic hidden Markov model for B cell receptor sequences

#### Summary

- antibodies develop within you via an evolutionary process
- understanding these evolutionary patterns is important for understanding how we respond to infection and vaccination
- we have found using Bayesian methods that evolutionary inferences are uncertain in this regime
- our most recent work develops a “Bayesian phylogenetic hidden Markov model,” which takes into account uncertainty in both the V(D)J recombination process and the evolutionary process
- this work reveals substantial amino-acid uncertainty in the inference of the unmutated common ancestor of VRC01, an important and heavily-studied anti-HIV antibody
- our results are described in a preprint which is now being revised for
*PLOS Computational Biology*

#### A brief description of antibody affinity maturation

In order to defend against a very large and ever-mutating pool of pathogens, your body randomly generates, and then optimizes, a large collection of antibodies. These antibodies are displayed as so-called *B cell receptors* on the surface of specialized B cells. The random generation is a process called V(D)J...
*(full post)*

### 24 Aug 2019 » Variational Bayesian phylogenetic inference

In late 2017 we were stuck without a clear way forward for our research on Bayesian phylogenetic inference methods.

We knew that we should be using gradient (i.e. multidimensional derivative) information to aid in finding the posterior, but couldn’t think of a way to find the *right* gradient. Indeed, we had recently finished our work on a variant of Hamiltonian Monte Carlo (HMC) that used the branch length gradient to guide exploration, along with a probabilistic means of hopping from one tree structure to another when a branch became zero. Although this project was a lot of fun and was an ICML paper, it wasn’t the big advance that we needed: these continuous branch length gradients weren’t contributing enough to the fundamental challenge of keeping the sampler in the good region of phylogenetic tree structures. But it was hard to even imagine a good solution to the central question: *how can we take gradients in the discrete space of phylogenetic trees?*

Meanwhile,...
*(full post)*

### 18 Jun 2019 » Bayesian phylogenetic inference without sampling trees

Most every description of Bayesian phylogenetics I’ve read proceeds as follows:

- “Bayesian phylogenetic analyses are conducted using a simulation technique known as Markov chain Monte Carlo (MCMC).” (Alfaro & Holder, 2006)
- “Posterior probabilities are obtained by exploring tree space using a sampling technique, called Markov chain Monte Carlo (MCMC).” (Lemey et al,
*The Phylogenetic Handbook*) - “Once the biologist has decided on the data, model and prior, the next step is to obtain a sample from the posterior. This is done by using MCMC…” (Nascimento et al, 2017.)

With statements like these in popular (and otherwise excellent!) reviews, it’s not surprising that people confuse Bayesian phylogenetics and Markov chain Monte Carlo (MCMC). Well, let’s be clear.

*MCMC is one way to approximate a Bayesian phylogenetic posterior distribution. It is not the only way.*

In this post I’ll describe two of our recent papers that together give a systematic, rather than random, means of approximating a phylogenetic posterior distribution.

Without a...
*(full post)*

### 05 Dec 2018 » Generalizing tree probability estimation via Bayesian networks

Posterior probability estimation of phylogenetic tree topologies from an MCMC sample is currently a pretty simple affair. You run your sampler, you get out some tree topologies, you count them up, normalize to get a probability, and done. It doesn’t seem like there’s a lot of room for improvement, right?

Wrong.

Let’s step back a little and think like statisticians. The posterior probability of a tree topology is an unknown quantity. By running an MCMC sampler, we get a histogram, the normalized version of which will converge to the true posterior in the limit of a large number of samples. We can use that simple histogram estimate, but nothing is stopping us from taking other estimators of the per-topology posterior distribution that may have nicer properties.

For real-valued samples we might use kernel density estimates to smooth noisy sampled distributions, which may reduce error when sampling is sparse. Because the number of phylogenies is huge, MCMC is computationally expensive, and we are naturally...
*(full post)*

### 15 May 2018 » Human T cell receptor occurrence patterns encode immune history, genetic background, and receptor specificity

High-throughput sequencing of our adaptive immune repertoires holds great promise for understanding immune state. These sequences implicitly contain a wealth of information on past and present exposures to infectious and autoimmune diseases, to environmental stimuli, and even to tumor-derived antigens. In principle, we should be able to use these sequences of rearranged receptors to infer their eliciting antigens, either individually or collectively.

We’re starting to see neat progress in these areas for T cell receptors (TCRs). Some recent studies compare TCR repertoire between individuals who do or do not have some immune state, such as an immunization, an autoimmune disease or a viral infection and work to find sequence-level differences between the repertoires. The Walczak-Mora team recently upped the bar by not requiring a control cohort. There has also been interesting progress on predicting epitope specificity from TCR sequence using structurally-informed sequence analysis.

Phil Bradley, just down the hall from us, wanted to take a different approach,...
*(full post)*

### 12 May 2018 » The Bayesian optimist's guide to adaptive immune receptor repertoire analysis

Immune receptor sequencing is stochastic through and through. We have cells with random V(D)J rearrangements that are stimulated through some random process of exposures, which lead to some random amount of expansion, and in the B cell case there is some random process of mutation and selection. So why don’t we use methods incorporating that uncertainty into our analysis?

We’ve tried to do this in our work, and have made some progress, but there is so much left to be done. When Sarah Cobey and Patrick Wilson kindly invited me to contribute to their special issue of *Immunological Reviews*, I knew I wanted to step back and ask:

*If computation was no barrier, how would we design an analysis framework that integrated out uncertainty in unknown quantities and took advantage of the hierarchical structure inherent in immune receptor data?*

I teamed up with Branden Olson, a Statistics PhD student in the lab, and went to work. It was a fun exercise to think...
*(full post)*

### 02 May 2018 » Benchmarking tree and ancestral sequence inference for B cell receptor sequences

Phylogenetic tools, in particular for ancestral sequence reconstruction, get used a lot in the B cell receptor (BCR) sequence analysis world. For example, they get used to reconstruct intermediate antibodies that then get synthesized in the lab and tested for binding (Wu et. al, 2011). But how well do phylogenetic tools work in this parameter regime? Although there have been countless benchmarking studies for phylogenetics, the case of B cell sequence evolution is different than the usual setting for phylogenetics:

- Sampling and sequencing, especially for direct sequencing of germinal centers, is dense compared to divergence between sequences. Because of the resulting distribution of short branch lengths, zero-length branches and multifurcations representing simultaneous divergence are common.
- The somatic hypermutation (SHM) process in affinity maturation is highly nucleotide-context-dependent process.
- Repertoire sequencing typically focuses on the coding sequence of antibodies, which are under very strong selective constraint. This contrasts with the neutral evolution assumptions of most phylogenetic algorithms, as well as the simulation...
*(full post)*

### 19 Apr 2018 » Predicting B cell receptor substitution profiles using public repertoire data

Can we predict how sites of an antibody will tolerate amino acid substitutions? Kristian Davidsen posed this question shortly after he arrived in my group, pointing out that being able to do such prediction would be quite useful. For example, engineered antibodies sometimes aggregate into clumps or have other properties that that make them useless for mass production. If we could figure out ways to change the amino acid sequence of an antibody without changing binding properties, that could help us avoid aggregation and make a more useful antibody.

How to start to address this complex and high-dimensional question? Although people have started to do deep mutational scanning on antibodies this type of data is hard to come by. On the other hand, B cell repertoire (i.e. antibody-coding) sequence data is becoming plentiful. B cells undergo affinity maturation to improve binding in collections of sequences called “clonal families” grouped by naive ancestor sequence (more background here). Although it’s not quite the...
*(full post)*

Complete list of all posts