T cell responses are initiated by antigen and promoted by a range of costimulatory signals. Understanding how T cells integrate alternative signal combinations and make decisions affecting immune response strength or tolerance poses a considerable theoretical challenge. Here, we report that T cell receptor (TCR) and costimulatory signals imprint an early, cell-intrinsic, division fate, whereby cells effectively count through generations before returning automatically to a quiescent state. This autonomous program can be extended by cytokines. Signals from the TCR, costimulatory receptors, and cytokines add together using a linear division calculus, allowing the strength of a T cell response to be predicted from the sum of the underlying signal components. These data resolve a long-standing costimulation paradox and provide a quantitative paradigm for therapeutically manipulating immune response strength.

T lymphocytes and B lymphocytes integrate activating signals to control the size of their proliferative response. Here we report that such control was achieved by timed changes in the production rate of cell-cycle-regulating proto-oncoprotein Myc, with division cessation occurring when Myc levels fell below a critical threshold. The changing pattern of the level of Myc was not affected by cell division, which identified the regulating mechanism as a cell-intrinsic, heritable temporal controller. Overexpression of Myc in stimulated T cells and B cells did not sustain cell proliferation indefinitely, as a separate 'time-to-die' mechanism, also heritable, was programmed after lymphocyte activation and led to eventual cell loss. Together the two competing cell-intrinsic timed fates created the canonical T cell and B cell immune-response pattern of rapid growth followed by loss of most cells. Furthermore, small changes in these timed processes by regulatory signals, or by oncogenic transformation, acted in synergy to greatly enhance cell numbers over time.

Stochastic variation in cell cycle time is a consistent feature of otherwise similar cells within a growing population. Classic studies concluded that the bulk of the variation occurs in the G 1 phase, and many mathematical models assume a constant time for traversing the S/G 2 /M phases. By direct observation of transgenic fluorescent fusion proteins that report the onset of S phase, we establish that dividing B and T lymphocytes spend a near-fixed proportion of total division time in S/G 2 /M phases, and this proportion is correlated between sibling cells. This result is inconsistent with models that assume independent times for consecutive phases. Instead, we propose a stretching model for dividing lymphocytes where all parts of the cell cycle are proportional to total division time. Data fitting based on a stretched cell cycle model can significantly improve estimates of cell cycle parameters drawn from DNA labeling data used to monitor immune cell dynamics.he kinetic relationship between phases of the cell cycle first came to attention with the advent of autoradiographic techniques for detecting DNA synthesis in the 1950s (1, 2). It was realized that such data could be used to resolve the dynamics of the proliferating population if combined with an appropriate cell cycle model. However, direct filming of times to divide revealed remarkable variation, even among cloned, presumed identical, cells (3-6), eliminating simple deterministic models as the basis for cell cycle control. Working toward developing a general model, Smith and Martin made the striking observation that plotting the proportion of undivided cells versus time (so-called "alpha plots"), gave curves suggestive of two distinct phases, one relatively constant and another stochastic (7). They proposed that the two phases mapped to discrete states of the cell cycle. A resting "A state," they suggested, was contained within the G 1 phase from which cells could exit with constant probability per unit time (analogous to radioactive decay). The cells then entered the "B phase," which includes that part of G 1 not included in A state, as well as the entirety of S/G 2 /M. In B phase, cells' activities were first described to be "deterministic, and directed towards replication," implying a constant B phase. However, in the same paper, this assumption was relaxed and the duration of B phase was described with a relatively constant random variable (7).Although details of the quantitative relationship and biological interpretation have been debated (7-12), the rule that the bulk of kinetic variation is in G 1 phase, and that time in S/G 2 /M is relatively fixed, is widely accepted. Furthermore, mathematical models adopting this mechanical description (so-called "transition probability" or "compartment" models) remain popular and form the basis of many studies of lymphocyte and cancer kinetics in vitro and in vivo today (13-21).More recently, a molecular description of cell cycle regulation, including the discovery of key regulatory proteins such as cyclins a...