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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.

In response to external stimuli, naïve B cells proliferate and take on a range of fates important for immunity. How their fate is determined is a topic of much recent research, with candidates including asymmetric cell division, lineage priming, stochastic assignment, and microenvironment instruction. Here we manipulate the generation of plasmablasts from B lymphocytes in vitro by varying CD40 stimulation strength to determine its influence on potential sources of fate control. Using long-term live cell imaging, we directly measure times to differentiate, divide, and die of hundreds of pairs of sibling cells. These data reveal that while the allocation of fates is significantly altered by signal strength, the proportion of siblings identified with asymmetric fates is unchanged. In contrast, we find that plasmablast generation is enhanced by slowing times to divide, which is consistent with a hypothesis of competing timed stochastic fate outcomes. We conclude that this mechanistically simple source of alternative fate regulation is important, and that useful quantitative models of signal integration can be developed based on its principles.

The busy period for a queue is cast as the area swept under the random walk until it first returns to zero. Encompassing non-i.i.d. increments, the large-deviations asymptotics of the busy period B is addressed, under the assumption that the increments satisfy standard conditions, including a negative drift. The main conclusions provide insight on the probability of a large busy period, and the manner in which this occurs. The scaled probability of a large busy period has the asymptote, for any b > 0, \begin{align*} \lim_{n\to\infty} \frac{1}{\sqrt{n}} \log P(B\geq bn) = -K\sqrt{b}, \end{align*} where \begin{align*} K = 2 \sqrt{-\int_0^{\lambda^*} \Lambda(\theta) \, d\theta}\,, \quad \hbox{with}\ \lambda^*=\sup\{\theta:\Lambda(\theta)\leq0\}, \end{align*} and with Λ denoting the scaled cumulant generating function of the increments process. The most likely path to a large swept area is found to be a simple rescaling of the path on [0, 1] given by ψ*(t) = −Λ(λ*(1 − t))/λ*. In contrast to the piecewise linear most likely path leading the random walk to hit a high level, this is strictly concave in general. While these two most likely paths have distinctly different forms, their derivatives coincide at the start of their trajectories, and at their first return to zero. These results partially answer an open problem of Kulick and Palmowski [18] regarding the tail of the work done during a busy period at a single server queue. The paper concludes with applications of these results to the estimation of the busy period statistics (λ*,K) based on observations of the increments, offering the possibility of estimating the likelihood of a large busy period in advance of observing one.

Cellular barcoding and other single-cell lineage-tracing strategies form experimental methodologies for analysis of in vivo cell fate that have been instrumental in several significant recent discoveries. Due to the highly nonlinear nature of proliferation and differentiation, interrogation of the resulting data for evaluation of potential lineage pathways requires a new quantitative framework complete with appropriate statistical tests. Here, we develop such a framework, illustrating its utility by analyzing data from barcoded multipotent cells of the blood system. This application demonstrates that the data require additional paths beyond those found in the classical model, which leads us to propose that hematopoietic differentiation follows a loss of potential mechanism and to suggest further experiments to test this deduction. Our quantitative framework can evaluate the compatibility of lineage trees with barcoded data from any proliferating and differentiating cell system.