Fig 1.
T-bet and GATA3 are the master transcription factors controlling Th1 and Th2 differentiation, respectively, and are confined within Th cells. IFNγ and IL-4 are the master cytokines controlling Th1 and Th2 differentiation, respectively, and are free to diffuse through the extracellular space. Together, expression of these four molecules are the four state variables of the dynamic model. Each of these four molecules can upregulate (arrow-head interactions) or downregulate (T-head interactions) the expression of the other molecules in the model. References to the immunological literature supporting the existence of the depicted interactions and their assigned parameter values are provided in S1 Table.
Fig 2.
The model captures the distribution of Th effector types in vitro in the presence and absence of cytokine signaling, due to an underlying bifurcation in the dynamical system.
All data are from [34]. Experiments and the model were both run at 2*106 cells/mL. (a) When cytokines accumulate unhindered, a uniform distribution of Th1, Th2, and mixed effector types is observed, as measured by the balance of T-bet and GATA3 expression, across 1000 sample paths of the SDE system. This closely matches empirical observations (inset). (b) When cytokine accumulation is blocked, a U-shaped distribution of Th1 and Th2 effector types is observed across 1000 sample paths of the SDE system. This also closely matches empirical observations (inset). (c) Analysis of the ODE system shows that mixed effector types are only stable in the presence of cytokine signaling. As cytokine secretion is removed from the model, the mixed effector type becomes unstable and bifurcates into polarized Th1 and Th2 effector types.
Fig 3.
The model predicts the dynamics of transcription factor expression under in vitro conditions with no exogeneous effector stimulation.
Experiment and model were both run at 2*106 cells/mL. Data are replotted from [34]. SDE mean and interquartile range are drawn from 1000 SDE sample paths.
Fig 4.
Th group polarization emerges as cell density increases, due to the changing relative strengths of within-scale vs. cross-scale molecular interactions.
(a) The stable effector balance among a group of Th cells transitions from mixed to polarized as the quorum cell density is surpassed. (b) The quorum cell density corresponds to a particular ratio of cytokine production: removal. (c) This cytokine production: removal ratio controls the ratio of cytokine: transcription factor expression at the mixed effector type equilibrium (y-axis is independent variable and x-axis is dependent variable). (d) The ratio of cytokine: transcription factor expression controls whether the net stabilizing effect of within-scale molecular interactions or the total destabilizing effect of cross-scale molecular interactions is stronger, and therefore whether the mixed equilibrium is stable or unstable.
Fig 5.
APCs spark and guide the Th quorum sensing process, but after enough time has passed, they cannot reverse the Th quorum decision.
(a) A representative scenario at biological cell density (109 cells/mL) in which 10 APCs enter a lymph node, six instructing for Th1 and four instructing for Th2. Even this small Th1 bias among APCs sparks a Th1-committed Th cell quorum. At some time marked by the grayscale dashed lines, the number of APCs increases to 1000, all instructing for Th2. This drastic switch can only reverse the commitment of the Th quorum if it occurs soon after initial arrival of APCs in the lymph node (here ~20 hr). (b) The time required for Th quorum commitment to become irreversible is most strongly controlled by the initial APC effector bias–the higher the percentage of APCs in favor of one effector type, the sooner the resulting Th quorum becomes irreversible. Timing is also impacted by the initial number of APCs–the larger the number of APCs, the sooner the resulting Th quorum becomes irreversible.
Fig 6.
Cell-to-cell variability in molecular (esp. cytokine) expression allows Th quora to discern when to switch effector types.
All simulations were run at 109 cells/mL. (a) Simulated time-courses of APC effector instruction may include transient and/or sustained changes in instruction (gray line), which Th quora ought to ignore and/or obey, respectively (black line). In the ODE model, Th quora cannot obey even sustained changes to APC instruction. (b) In the SDE model with low levels of variability, Th quora struggle to obey sustained changes to APC instruction. Twenty sample paths along with their mean and median (shades of green) are shown. (c) Medium levels of variability permit discernment by ignoring transient changes to APC instruction but obeying sustained changes. (d) High levels of variability begin to diminish discernment. (e) Th discernment peaks for intermediate levels of stochasticity in molecular expression, regardless of sensitivity (i.e. how long a change in APC instruction must last before it is considered “sustained”). Percentage volatility = 100*nTF1 = 100*nTF2 = 100*nCY1 = 100*nCY2. Relative performance scores how well Th quora tracked the theoretically optimal response, relative to the quorum that did best, across 200 randomly generated time-courses of APC instruction. (f) The analysis shown in (e) was repeated, but where nTF1 = nTF2 need not equal nCY1 = nCY2. Data from (e) appear along the diagonal; new data are contained off the diagonal. Th quora perform best when stochasticity in cytokine expression is high, and stochasticity in transcription factor expression is low.
Fig 7.
Orange circles represent Th1 cells, blue circles represent Th2 cells, and other shades represent Th1-Th2 hybrid cells. The large gray shapes represent APCs, or experimentally provided effector stimulation. (a) At 106 cells/mL with no dynamic cytokine signaling, individual neighboring Th cells adopt oppositely polarized effector types. (b) At 106 cells/mL with dynamic cytokine signaling, oppositely polarized Th cells cause each other to become Th1-Th2 hybrids. (c) At 109 cells/mL with dynamic cytokine signaling, mixed effector types resolve into fully polarized Th1 or Th2 groups, via quorum sensing. Initial polarization by APCs, effector hybrid formation as cytokines dynamically accumulate, and quorum emergence as cytokines accumulate further and APCs are ignored, may define 3 phases of Th effector differentiation in vivo.