Design principles of the cytotoxic CD8+ T-cell response

TL;DR

The study treats the CD8$^+$ T-cell response as a feedback-controlled decision process that integrates the instantaneous antigen cue $\sigma_{\text{Ag}}$ with cumulative harm signals $\sigma_{\text{inf}}$ and $\sigma_{\text{res}}$ to regulate activation, expansion, differentiation, and contraction. By exploring a broad class of signal-processing designs and optimizing for rapid pathogen clearance while minimizing immunopathology, it uncovers a Pareto trade-off and characterizes four archetypes of infection responses that reproduce macro-dynamics of T-cell expansion and point to design principles for cancer immunotherapy. The authors show that optimal designs tend to be antigen-driven with an anti-inflammatory brake, and that near-elbow designs can generalize across archetypes, explaining how endogenous programs may balance infection control with autoimmunity risk. Extending the framework to cancer immunotherapy, the work analyzes how antigenicity, T-cell dosage, and engineered perturbations to baseline regulatory programs can shift the trade-off toward more robust tumor clearance while constraining collateral damage. Overall, the results provide a principled control-theory view of cytotoxic T-cell decision-making and offer actionable targets for engineering T-cell therapies with improved efficacy and safety.

Abstract

Cytotoxic T lymphocytes eliminate infected or malignant cells, safeguarding surrounding tissues. Although experimental and systems-immunology studies have cataloged many molecular and cellular actors involved in an immune response, the design principles governing how the speed and magnitude of T-cell responses emerge from cellular decision-making remain elusive. Here, we recast the T-cell response as a feedback-controlled program, wherein the rates of activation, proliferation, differentiation and death are regulated through antigenic, pro- and anti-inflammatory cues. By exploring a broad class of feedback-controller designs as potential immune programs, we demonstrate how the speed and magnitude of T-cell responses emerge from optimizing signal-feedback to protect against diverse infection settings. We recover an inherent trade-off: infection clearance at the cost of immunopathology. We show how this trade-off is encoded into the logic of T-cell responses by hierarchical sensitivity to different immune signals. Notably, we find that designs that balance harm from acute infections and autoimmunity produce immune responses consistent with experimentally observed patterns of T-cell effector expansion in mice. Extending our model to immune-based T-cell therapies for cancer tumors, we identify a trade-off between the affinity for tumor antigens ("quality") and the abundance ("quantity") of infused T-cells necessary for effective treatment. Finally, we show how therapeutic efficacy can be improved by targeted genetic perturbations to T-cells. Our findings offer a unified control-logic for cytotoxic T-cell responses and point to specific regulatory programs that can be engineered for more robust T-cell therapies.

Figures (6)

• Figure 1: CD8$^+$ T-cell response to infections.(A) The schematic shows how upon infection, susceptible cells $S$ become infected $I$ at rate $b_I$. Infected cells provide an antigen signal $\sigma_\text{Ag} \propto I$, and die at rate $d_I$, which triggers an infection harm signal $\sigma_\text{inf}$. In response to infection, naïve CD8$^+$ T-cells (with initial clone size of $N_\text{lin.}$) are activated $N\to N^*$, and can then differentiate into effector or memory fates (Fig. S1). Effector cells can proliferate and kill infected and bystander cells, generating a response-harm signal $\sigma_\text{res}$, and finally become terminal or differentiate into memory. Consequently, T-cell transitions are modulated by the threes signals ($\sigma_\text{Ag},\sigma_\text{inf},\sigma_\text{res}$). Infection dynamics $(S,I)$ are modeled by ODEs coupled to a stochastic dynamics of the T-cell response. Memory transitions (gray arrows) are neglected in our model. (B) Representative trajectories of susceptible, infected, effector, and memory CD8$^+$ T-cells are shown over time. (C) Each T-cell transition has a rate $r_i = r^\text{max} g_i (\sigma_\text{Ag}, \sigma_\text{inf}, \sigma_\text{res}; \vec{\psi},\ell)$, modulated by a sigmoidal function with baseline $\ell$ and signal sensitivities $\vec{\psi}$ (eqs. \ref{['eq:rate_regulation']}, \ref{['eq:monod']}). The regulatory parameters define the design of the effector program $\vec{\theta}$ (eq. \ref{['eq:theta']}). (D) We assess design performance over diverse infections sampled from a broad range of reproduction numbers $R_0$ (eq. \ref{['eq:R_0']}) and immunogenicities $\kappa$ (eq. \ref{['eq:kappa']}). For each infection, we can find an optimal design $\vec{\theta}^{(\mathrm{min})}$ that minimizes total cell loss (harm). Harm decomposes into infection harm $H_\text{inf.}$ (cells killed by the pathogen plus infected cells eliminated by effectors), and toxicity $H_\text{toxic.}$ (healthy bystanders killed by effectors), highlighting an intrinsic trade-off (eq. \ref{['eq: clear_tox']}). Simulation parameters in (B): $S_\text{max} = 10^7, N_\text{lin.} = 100, K_I = 10^{-3}S_\text{max}, K_S = S_\text{max}, K_H = 10^{-3}S_\text{max}, b_I = 2.0\times10^{-7} \text{day}^{-1}~\text{per cell},d_I = 0.5~\text{day}^{-1}, I_0 = 10^{-4}S_\text{max}, \vec{\theta} =(\psi_{Ag} = 2, \psi_{I} = 2, \psi_{E} = -0.25, \ell_{N \to N^*} = -0.75,\ell_{N^*\to E} = -0.75,\ell_{E\to \emptyset} = 0.75$).
• Figure 2: Design parameters shape T-cell response and infection clearance.(A) Varying the design parameters influences effector trajectories. (B) Trajectories are shown for the population size of effectors (top) and infected cells (bottom), measured in units of maximum number of susceptible cells $S_\text{max}$, for designs that vary a single baseline transition rate $g_{0,i}$ (color) indicated atop each panel. All other design parameters are fixed at: fast activation, $g_{0,N \to N^*} = 0.95$; fast differentiation, $g_{0,N^* \to E} = 0.95$; slow contraction, $g_{0,E\to \emptyset} = 0.05$; and zero signal feedback, $\psi_{\text{Ag}} =\psi_\text{inf} =\psi_\text{res} = 0$. Trajectories reflecting the impact of varying signal sensitivities $\psi$'s are shown in SI Appendix, Fig. S2. (C) Peak effector count, measured in units of maximum number of susceptible cells $S_\text{max}$, is shown by varying each of the three baseline transition rates (colors), while keeping the rest of the parameters fixed (similar to (B)). Parameters are the same as Fig. \ref{['fig1']}, except for $K_I = 10^{-2}S_\text{max}$.
• Figure 3: Toxicity-infection harm trade-off across T-cell regulatory designs.(A) Density plots of toxicity $H_\text{toxic.}$ versus infection harm $H_\text{inf.}$ (eq. \ref{['eq: clear_tox']})---measured in units of $S_\text{max}$---for $4.8\times 10^6$ T-cell regulatory designs, $\vec{\theta}$, uniformly grid-sampled across four infection scenarios (panels; columns: $\kappa= 5.6$ (left), $\kappa= 178$ (right); rows: $R_0 = 2.5$ (bottom), $R_0 = 5.0$ (top)). Designs are sampled uniformly across signal sensitivities $\psi\,\text{'s} \in[-3,3]$ and baseline rates $\ell\,\text{'s} \in[-3,3]$ (eq. \ref{['eq:theta']}). Infection scenarios are sampled by changing $K_I$ and $b_I$, while holding $S_{\max}$, $d_I$, and $K_S$ fixed. Black points denote no-feedback designs ($\vec{\psi}=0$), and the large magenta circle in each panel marks the design that minimizes total harm, $\vec{\theta}^{(\mathrm{min})}$. (B) For many different infection scenarios $(\kappa,R_0)$, we identify an ensemble of near-optimal designs $\Theta(\kappa,R_0)$, whose total harm is within $10^{-2}\times S_\text{max}$ of the minimum sampled total harm (as in the magenta point in A). By computing the ensemble-averaged design parameters $\langle\vec{\theta}\rangle_{\Theta(\kappa,R_0)}$ for each infection scenario, and using these averages to cluster infections, we identify four infection "archetypes" (colors): I--IV, as indicated (SI Appendix). (C) Toxicity vs. infection harm associated with optimal designs for each archetype is shown. Large dots represent cluster averages and small transparent dots represent individual infections, sampled in (B). (D) Bars indicate the ensemble-mean of design parameters, $\langle\vec{\theta}\rangle_{\Theta^{(i)}}$, computed by identifying the ensemble of designs ${\Theta^{(i)}}$ which minimize cluster-averaged total harm for archetype $i$ to within $10^{-2}\times S_\text{max}$ of the minimum sampled cluster-averaged total harm (similar to (B)). Error bars denote the standard deviation within this ensemble. All design variables are normalized by their respective bounds ($\psi^{\max}=3$, $\ell^{\max}=3$). Unless otherwise noted, simulation parameters: $S_\text{max} = 10^7, N_\text{lin.} = 10^{-5}S_\text{max}, K_S = S_\text{max}, K_H = 10^{-3}S_\text{max}, d_I = 0.5~\text{day}^{-1}, I_0 = 10^{-4}S_\text{max}.$
• Figure 4: Pareto-optimal designs balancing harm from acute infections and autoimmunity.(A) Bi-objective optimization to minimize the weighted sum of harms associated with T-cell regulatory designs $\vec{\theta}$ across two infection archetypes ($A,B$) yields a Pareto front (magenta curve); eq. \ref{['eq: pareto optimization']}. Points on the curve are Pareto-optimal designs, parameterized by the weight $\lambda \in [0,1]$, quantifying the emphasis on archetype B; moving left to right corresponds to decreasing $\lambda$ (less emphasis on B). (B) The density plot shows harms incurred by $4.8\times 10^6$ uniformly sampled designs in their response to archetype I (non-replicating, self-like/ auto-immune inducing or allergenic antigens; $R_0=1$) versus archetype II (immunogenic infection; high $\kappa$), as defined in Fig. \ref{['fig3']}B. Designs are sampled on a uniform Cartesian grid of sensitivities $\psi_\sigma\in[-3,3]$ and baseline rates $\ell_i\in[-3,3]$ (as in Fig. \ref{['fig3']}A). For many values of $\lambda$, we minimize the objective in (A), and trace out the Pareto front (magenta). For each point $\lambda$ on the front, we identify the ensemble of designs closest to the Pareto front ($\Theta(\lambda)$), where a design belongs to the near-Pareto ensemble at $\lambda$ if its incurred harm against archetypes I and II simultaneously lie within 5% of the $\lambda$-Pareto-optimal harm of the respective archetypes. The black square indicates the elbow of the Pareto curve $\lambda^*$: the point where further reductions in archetype-I harm incur larger increases in archetype-II harm (see SI Appendix). The average design parameter values over the near-elbow ensemble are $\langle \vec{\theta}\rangle_{\Theta(\lambda^*)}=(2.89,1.67,-0.67,-0.22,-1.94,0.94)$. (C) Decomposition of total harm along the Pareto front in (B) into infection-related harm and toxicity (eq. \ref{['eq: clear_tox']}). The black dashed line indicates the position of the elbow from (B). (D) Solid lines show parameter magnitudes for the signal sensitivities $\psi$ (left) and the baseline rates $g_0(\ell)$ (right), each scaled to variable bounds $(\psi^{\max}=3,\ \ell^{\max}=3)$, as a function of harm incurred under archetype II along the Pareto curve (parameterized by $\lambda$). Shaded envelopes denote the standard deviation of the near-Pareto ensemble of designs $\Theta(\lambda),~\lambda \in [0,1]$ traced out by the Pareto front. (E) For each archetype in Fig. \ref{['fig3']}B, total harm is shown for the archetype-specific minimizer $\vec{\theta}^{(\mathrm{min})}$ (circle) and for the average over near-elbow ensemble in (B). See SI Appendix, Figs. S6, S7 for Pareto fronts formed by other pairs of archetypes. All simulation parameters other than the varied $K_I$, $b_I$, and $\vec{\theta}$ match Fig. \ref{['fig1']}.
• Figure 5: Elbow-optimal designs recapitulating macro-dynamics of T-cell expansion.(A,B) Fold expansion (i.e, peak clone size divided by the initial precursor number) of antigen-specific CD8$^+$ T-cells in mice plotted against (A) the initial precursor number (data from Badovinac2007-ii), and (B) the relative pMHC concentration required for half-maximal activation EC$_{50}$ (data from Zehn2009-up); in our model, EC$_{50}$ is proxied by $K_I$. (C,D) Simulated mean fold expansion for designs belonging to the near-elbow ensemble from Fig. \ref{['fig4']}B ($\Theta(\lambda^*)$) when their sensitivity to the infection-harm signal ($\psi_{\text{inf}}$) is varied (colors), shown as a function of (C) the initial precursor T-cell number, and (D) the immunogenicity of the antigen $\kappa$. For each design in the near-elbow ensemble identified in Fig. \ref{['fig4']}, $\vec{\theta} \in \Theta(\lambda^*)$, we change $\psi_\text{inf} \to c\times \psi_\text{inf}$ for constants $c \in \{0, 0.1,1.0\}$ (colors), and simulate responses against the broad sample of infections (Fig. \ref{['fig3']}B). Trend lines are obtained by averaging over infections and designs in the near-elbow ensemble (SI Appendix, Figs. S8, S9). Elbow designs with reduced sensitivity to infection-derived harm qualitatively match the experimental macro-dynamics of T-cell expansion. Unless otherwise indicated, simulation parameters: $S_\text{max} = 10^7, K_S = S_\text{max}, K_H = 10^{-3}S_\text{max}, d_I = 0.5~\text{day}^{-1}, I_0 = 10^{-4}S_\text{max}$.