Modeling of cytometry data in logarithmic space: When is a bimodal distribution not bimodal?

Abstract

Recent efforts in systems immunology lead researchers to build quantitative models of cell activation and differentiation. One goal is to account for the distributions of proteins from single-cell measurements by flow cytometry or mass cytometry as readout of biological regulation. In that context, large cell-to-cell variability is often observed in biological quantities. We show here that these readouts, viewed in logarithmic scale may result in two easily-distinguishable modes, while the underlying distribution (in linear scale) is unimodal. We introduce a simple mathematical test to highlight this mismatch. We then dissect the flow of influence of cell-to-cell variability proposing a graphical model which motivates higher-dimensional analysis of the data. Finally we show how acquiring additional biological information can be used to reduce uncertainty introduced by cell-to-cell variability, helping to clarify whether the data is uni- or bimodal. This communication has cautionary implications for manual and automatic gating strategies, as well as clustering and modeling of single-cell measurements. © 2018 International Society for Advancement of Cytometry.

CD49d promotes disease progression in chronic lymphocytic leukemia: new insights from CD49d bimodal expression

“…Immunophenotypic analyses and cell sortings were performed on fresh PB, or paired PB and bone marrow (BM) samples at different time points using a FACSCanto I and a FACSAriaIII (BD Biosciences, La Jolla, CA) flow cytometer/cell sorter upon instrument calibration with CS&T beads (BD Biosciences) using the FACSDiva software (BD Biosciences). Detailed guidelines for the analysis and definition of CD49d bimodal expression 28 are reported in supplemental Materials and methods.…”

Critical slowing down in biochemical networks with feedback

“…The application of our methodology to these experiments serves as a proof of concept, and questions remain with regard to the interpretation of the experimental data. For example, here we do not address the wellknown question of the role of cell-to-cell variability in the broadening of immune cell distributions [40,41]. Although critical slowing down has been observed in yeast [42,43], it remains an open question whether cell-to-cell variability dominates dynamics in mammalian cells.…”

Biochemical feedback and its application to immune cells II: dynamics and critical slowing down

“…The theory we present here assumes only intrinsic birth-death reactions and neglects more complex mechanisms such as bursting [36,37], parameter fluctuations [38,39], or cell-to-cell variability [40,41] that may play an important role in the immune cells. Nonetheless, similar models that also focus only on intrinsic noise have suc-cessfully described ppERK in T cells in the past [42,43].…”