Cyton2: A Model of Immune Cell Population Dynamics That Includes Familial Instructional Inheritance

Abstract

Lymphocytes are the central actors in adaptive immune responses. When challenged with antigen, a small number of B and T cells have a cognate receptor capable of recognising and responding to the insult. These cells proliferate, building an exponentially growing, differentiating clone army to fight off the threat, before ceasing to divide and dying over a period of weeks, leaving in their wake memory cells that are primed to rapidly respond to any repeated infection. Due to the non-linearity of lymphocyte population dynamics, mathematical models are needed to interrogate data from experimental studies. Due to lack of evidence to the contrary and appealing to arguments based on Occam’s Razor, in these models newly born progeny are typically assumed to behave independently of their predecessors. Recent experimental studies, however, challenge that assumption, making clear that there is substantial inheritance of timed fate changes from each cell by its offspring, calling for a revision to the existing mathematical modelling paradigms used for information extraction. By assessing long-term live-cell imaging of stimulated murine B and T cells in vitro, we distilled the key phenomena of these within-family inheritances and used them to develop a new mathematical model, Cyton2, that encapsulates them. We establish the model’s consistency with these newly observed fine-grained features. Two natural concerns for any model that includes familial correlations would be that it is overparameterised or computationally inefficient in data fitting, but neither is the case for Cyton2. We demonstrate Cyton2’s utility by challenging it with high-throughput flow cytometry data, which confirms the robustness of its parameter estimation as well as its ability to extract biological meaning from complex mixed stimulation experiments. Cyton2, therefore, offers an alternate mathematical model, one that is, more aligned to experimental observation, for drawing inferences on lymphocyte population dynamics.

Counting generations in birth and death processes with competing Erlang and exponential waiting times

“…In particular, no fate correlation is assumed between daughter cells and their progenitors, or between siblings. However, data sets from time-lapse microscopy of B and T cell families 10 – 12 , 14 , 16 , 17 , 25 show that division and death times for siblings are correlated, and “division destiny” is a familial characteristic 24 . A further potential extension of the MS-G model is the introduction of a population carrying capacity.…”

“…The cyton model is a general framework for modelling proliferating lymphocytes, based on the idea that each cell has a set of competing clocks, determining its fate 13 . A number of features are incorporated in the model: generation-dependent parameters, heritable factors, and correlations between cells of the same generation 11 , 16 , 24 . When the fate of an individual cell is determined by competing internal clocks, the probability density of observed times between divisions is not the same as that of the division clock because division only happens if another fate does not.…”

Fate Bias and Transcriptional Memory of human B cells

“…We call the genes we identified clonally coherent genes (CCGs). One way to intuitively understand these clonal effects is to observe the cascade plot of the putative CCG, for example IGKC (4A) (Cheon et al, 2021). A clear clonal structure of high expressing clones and low expressing clones is scrambled upon permuting clonal labels.…”

“…In vitro , a researcher can control most extrinsic factors, such as cell density, cytokine cocktails, and media compositions, allowing them to study cell-intrinsic differentiation programs. In the case of B and T cells, (Cheon et al 2021) well-controlled extrinsic conditions still reliably generate a large diversity of cell fates, indicating a strong contribution of intrinsic cell diversity to population-level diversity seen in vivo . The question of how gene expression responds to extracellular stimuli, while a cell maintains its erstwhile identity is generally poorly understood.…”

Lineage tracing reveals fate bias and transcriptional memory in human B cells

“…In vitro, a researcher can control most extrinsic factors, such as cell density, cytokine cocktails, and media compositions, allowing them to study cell-intrinsic differentiation programs. In the case of B and T cells, well-controlled extrinsic conditions still reliably generate a large diversity of cell fates, indicating a strong contribution of intrinsic cell diversity to population-level diversity seen in vivo ( Cheon et al, 2021 ). The question of how gene expression responds to extracellular stimuli, while a cell maintains its identity, is generally poorly understood.…”