Cytometry at time-of-flight (CyTOF)

• Commercialized in 2009

• Makes use of time-of-flight spectrometry to accelerate, separate, and identify ions by mass

• Enables detection of many parameters (biological, phenotypic, or functional markers) in less time and at a higher resolution

• Led to greater understanding of natural killer (NK) cells

Natural Killer Cells

• Natural Killer cells play a critical role in cancer immunosurveillance.

• NK cell diversity affects antiviral response.

• Drs. Thall and Rezvani, at MD Anderson Cancer Center, have conducted clinical trials to study the potential clinical efficacy of umbilical cord blood (UCB) transplantation as a therapy for leukemia.

• UCB NK cell therapy has the advantage of low risk of viral transmission from donor to recipient .

• In the trials, leukemia patients received UCB cell transplants, and NK cell surface markers are measured using mass cytometry.

CyTOF Data

CyTOF Data

Obtaining cell subpopulations using overly-simplistic may yield an unreasonably high number of subpopulations.

Objective

Existing Methods

• Most existing methods use traditional clustering methods (K-means, hierarchical clustering, density-based clustering, nearest-neighbor clustering, etc.)

• For high-dimensional cytometry data, compared existing clustering methods including FlowSOM , PhenoGraph , Rclusterpp , and flowClust .

• Existing methods do not directly model latent subpopulations or quantify model uncertainty

Bayesian Feature Allocation Model for Heterogeneous Cell Populations – Notation

• $I$: Number of samples
• $J$: Number of markers
• $N_i$: Number of observations in sample $i$.
• $y_{i,n,j}$: Raw expression levels for observation $n$, in samples $i$, for marker $j$. (For $ỹ_{i,n,j} \ge 0$)
• $c_{i,j}$: Cutoff for marker $j$, sample $i$
• $y_{i,n,j}$: Transformed expression levels for observation $n$, sample $i$, marker $j$

  \[y_{i,n,j}=\log(\tilde{y}_{i,n,j}/c_{i,j}) \in \mathbb{R}.\]

  • $(y_{i,n,j} \gg 0)$ likely corresponds to expression
  • $(y_{i,n,j} \ll 0)$ likely corresponds to non-expression

Bayesian Feature Allocation Model for Heterogeneous Cell Populations

• $\bm Z$: $(J \times K)$ binary matrix defining the latent subpopulations.
  • if $Z_{j,k} = 1$, then marker $j$ is expressed in subpopulation $k$
  • if $Z_{j,k} = 0$, then marker $j$ is not expressed in subpopulation $k$

• $K$ is a sufficiently large constant

• $\lambda_{i,n} \in \{1,…,K\}$: The latent subpopulation of observation $n$, sample $i$

Sampling Distribution

• $F_{0,i,j} = \sum_{\ell=1}^{L^0} \eta^0_{i,j,\ell} \cdot \text{Normal}(\mu^\star_{0,\ell}, \sigma^2_i)$
• $F_{1,i,j} = \sum_{\ell=1}^{L^1} \eta^1_{i,j,\ell} \cdot \text{Normal}(\mu^\star_{1,\ell}, \sigma^2_i)$

Figure 2: Kernel density estimate of samples from $F_0$ (blue) and $F_1$ (red).

$$\int_0^\infty \theta e^{-\theta x} dx = 1$$

References