T-cell activation: A queuing theory analysis at low agonist density

Modelling the interplay between the CD4[Formula: see text]/CD8[Formula: see text] T-cell ratio and the expression of MHC-I in tumours

Describing the anti-tumour immune response as a series of cellular kinetic reactions from known immunological mechanisms, we create a mathematical model that shows the CD4[Formula: see text]/CD8[Formula: see text] T-cell ratio, T-cell infiltration and the expression of MHC-I to be interacting factors in tumour elimination. Methods from dynamical systems theory and non-equilibrium statistical mechanics are used to model the T-cell dependent anti-tumour immune response. Our model predicts a critical level of MHC-I expression which determines whether or not the tumour escapes the immune response. This critical level of MHC-I depends on the helper/cytotoxic T-cell ratio. However, our model also suggests that the immune system is robust against small changes in this ratio. We also find that T-cell infiltration and the specificity of the intra-tumour TCR repertoire will affect the critical MHC-I expression. Our work suggests that the functional form of the time evolution of MHC-I expression may explain the qualitative behaviour of tumour growth seen in patients.

Modeling of an immune response: Queuing network analysis of the impact of zinc and cadmium on macrophage activation

Chronic obstructive pulmonary disease is characterized by progressive, irreversible airflow obstruction resulting from an abnormal inflammatory response to noxious gases and particles. Alveolar macrophages rely on the transcription factors, nuclear factor κB and mitogen-activated protein kinase, among others, to facilitate the production of inflammatory mediators designed to help rid the lung of foreign pathogens and noxious stimuli. Building a kinetic model using queuing networks, provides a quantitative approach incorporating an initial number of individual molecules along with rates of the reactions in any given pathway. Accordingly, this model has been shown useful to model cell behavior including signal transduction, transcription, and metabolic pathways. The aim of this study was to determine whether a queuing theory model that involves lipopolysaccharide-mediated macrophage activation in tandem with changes in intracellular Cd and zinc (Zn) content or a lack thereof, would be useful to predict their impact on immune activation. We then validate our model with biologic cytokine output from human macrophages relative to the timing of innate immune activation. We believe that our results further prove the validity of the queuing theory approach to model intracellular molecular signaling and postulate that it can be useful to predict additional cell signaling pathways and the corresponding biological outcomes.

Adaptive T cell immunotherapy in cancer

Impaired tumor-specific effector T cells contribute to tumor progression and unfavorable clinical outcomes. As a compensatory T cell-dependent cancer immunoediting strategy, adoptive T cell therapy (ACT) has achieved encouraging therapeutic results, and this strategy is now on the center stage of cancer treatment and research. ACT involves the ex vivo stimulation and expansion of tumor-infiltrating lymphocytes (TILs) with inherent tumor reactivity or T cells that have been genetically modified to express the cognate chimeric antigen receptor or T cell receptor (CAR/TCR), followed by the passive transfer of these cells into a lymphodepleted host. Primed T cells must provide highly efficient and long-lasting immune defense against transformed cells during ACT. Anin-depth understanding of the basic mechanisms of these living drugs can help us improve upon current strategies and design better next-generation T cell-based immunotherapies. From this perspective, we provide an overview of current developments in different ACT strategies, with a focus on frontier clinical trials that offer a proof of principle. Meanwhile, insights into the determinants of ACT are discussed, which will lead to more rational, potent and widespread applications in the future.

COMPARISON OF A DUAL STRATEGY FOR T-CELL ACTIVATION UNDER INHIBITION OF THE CD4 RECEPTOR

We consider a stochastic model for T-cell activation proposed in Refs. [1] and [2] to compare the specificity and sensitivity of two different strategies for T-cell activation that utilize the history of phosphorylation of T-cell receptor (TCR). We compare these two strategies when the temporal signals/events that are essential for progressive T-cell activation are suppressed by blockade of CD4 receptor that may have caused by disease or therapeutic effects.3–6 We show that under these conditions, a threshold-strategy which is capable of maintaining a threshold (for total number of phosphorylated TCRs by time [Formula: see text]) for a further duration [Formula: see text] performs better in discriminating agonist peptides than a single-threshold strategy (reached by time [Formula: see text]) leading to T-cell activation using the Wentzell-Friedlin theory for large deviations for stochastic processes.7,8

Analysis of Cell Signal Transduction Based on Kullback-Leibler Divergence: Channel Capacity and Conservation of Its Production Rate during Cascade

Kullback–Leibler divergence (KLD) is a type of extended mutual entropy, which is used as a measure of information gain when transferring from a prior distribution to a posterior distribution. In this study, KLD is applied to the thermodynamic analysis of cell signal transduction cascade and serves an alternative to mutual entropy. When KLD is minimized, the divergence is given by the ratio of the prior selection probability of the signaling molecule to the posterior selection probability. Moreover, the information gain during the entire channel is shown to be adequately described by average KLD production rate. Thus, this approach provides a framework for the quantitative analysis of signal transduction. Moreover, the proposed approach can identify an effective cascade for a signaling network.

A stochastic T cell response criterion

The adaptive immune system relies on different cell types to provide fast and coordinated responses, characterized by recognition of pathogenic challenge, extensive cellular proliferation and differentiation, as well as death. T cells are a subset of the adaptive immune cellular pool that recognize immunogenic peptides expressed on the surface of antigen-presenting cells by means of specialized receptors on their membrane. T cell receptor binding to ligand determines T cell responses at different times and locations during the life of a T cell. Current experimental evidence provides support to the following: (i) sufficiently long receptor–ligand engagements are required to initiate the T cell signalling cascade that results in productive signal transduction and (ii) counting devices are at work in T cells to allow signal accumulation, decoding and translation into biological responses. In the light of these results, we explore, with mathematical models, the timescales associated with T cell responses. We consider two different criteria: a stochastic one (the mean time it takes to have had N receptor–ligand complexes bound for at least a dwell time, τ, each) and one based on equilibrium (the time to reach a threshold number N of receptor–ligand complexes). We have applied mathematical models to previous experiments in the context of thymic negative selection and to recent two-dimensional experiments. Our results indicate that the stochastic criterion provides support to the thymic affinity threshold hypothesis, whereas the equilibrium one does not, and agrees with the ligand hierarchy experimentally established for thymic negative selection.

Network-of-queues approach to B-cell-receptor affinity discrimination

The immune system is one of the most complex signal processing machineries in biology. The adaptive immune system, consisting of B and T lymphocytes, is activated in response to a large spectrum of pathogen antigens. B cells recognize and bind the antigen through B-cell receptors (BCRs) and this is fundamental for B-cell activation. However, the system response is dependent on BCR-antigen affinity values that span several orders of magnitude. Moreover, the ability of the BCR to discriminate between affinities at the high end (e.g., 10^{9}M^{-1}-10^{10}M^{-1}) challenges the formulation of a mathematical model able to robustly separate these affinity-dependent responses. Queuing theory enables the analysis of many related processes, such as those resulting from the stochasticity of protein binding and unbinding events. Here we define a network of queues, consisting of BCR early signaling states and transition rates related to the propensity of molecular aggregates to form or disassemble. By considering the family of marginal distributions of BCRs in a given signaling state, we report a significant separation (measured as Jensen-Shannon divergence) that arises from a broad spectrum of antigen affinities.

Mediation of T-cell activation by actin meshworks

Although the actin cytoskeleton and T-cell receptor (TCR) signaling complexes are seemingly distinct molecular structures, they are tightly integrated in T cells. The signaling pathways initiated by TCRs binding to peptide MHC complexes are extensively influenced by the actin cytoskeletal activities of the motile phase before TCR signaling, the signalosome scaffolding function of the cytoskeleton, and the translocation of signaling clusters that precedes the termination of signaling at these complexes. As these three successive phases constitute essentially all the steps consequent to immune synapse formation, it has become clear that the substantial physical forces and signaling interactions generated by the actin cytoskeleton dominate the signaling life cycle of TCR signalosomes. We discuss the contributions of the actin cytoskeleton to TCR signaling phases and model some remaining questions about how specific cytoskeletal factors regulate TCR signaling outcomes.

Early T-cell activation biophysics

The T-cell is one of the main players in the mammalian immune response. It ensures antigen recognition at the surface of antigen-presenting cells in a complex and highly sensitive and specific process, in which the encounter of the T-cell receptor with the agonist peptide associated with the major histocompatibility complex triggers T-cell activation. While signaling pathways have been elucidated in increasing detail, the mechanism of TCR triggering remains highly controversial despite active research published in the past 10 years. In this paper, we present a short overview of pending questions on critical initial events associated with T-cell triggering. In particular, we examine biophysical approaches already in use, as well as future directions. We suggest that the most recent advances in fluorescence super-resolution imaging, coupled with the new classes of genetic fluorescent probes, will play an important role in elucidation of the T-cell triggering mechanism. Beyond this aspect, we predict that exploration of mechanical cues in the triggering process will provide new clues leading to clarification of the entire mechanism.

Stochastic effects and bistability in T cell receptor signaling

The stochastic dynamics of T cell receptor (TCR) signaling are studied using a mathematical model intended to capture kinetic proofreading (sensitivity to ligand-receptor binding kinetics) and negative and positive feedback regulation mediated, respectively, by the phosphatase SHP1 and the MAP kinase ERK. The model incorporates protein-protein interactions involved in initiating TCR-mediated cellular responses and reproduces several experimental observations about the behavior of TCR signaling, including robust responses to as few as a handful of ligands (agonist peptide-MHC complexes on an antigen-presenting cell), distinct responses to ligands that bind TCR with different lifetimes, and antagonism. Analysis of the model indicates that TCR signaling dynamics are marked by significant stochastic fluctuations and bistability, which is caused by the competition between the positive and negative feedbacks. Stochastic fluctuations are such that single-cell trajectories differ qualitatively from the trajectory predicted in the deterministic approximation of the dynamics. Because of bistability, the average of single-cell trajectories differs markedly from the deterministic trajectory. Bistability combined with stochastic fluctuations allows for switch-like responses to signals, which may aid T cells in making committed cell-fate decisions.

Coreceptor CD8-driven modulation of T cell antigen receptor specificity

The CD8 coreceptor modulates the interaction between the T cell antigen receptor (TCR) and peptide-major histocompatibility class I (pMHCI). We present evidence that CD8 not only modifies the affinity of cognate TCR/pMHCI binding by altering both the association rate and the dissociation rate of the TCR/pMHCI interaction, but modulates the sensitivity (triggering threshold) of the TCR as well, by recruiting TCR/pMHCI complexes to membrane microdomains at a rate which depends on the affinity of MHCI/CD8 binding. Mathematical analysis of these modulatory effects indicates that a T cell can alter its functional avidity for its agonists by regulating CD8 expression, and can rearrange the relative potencies of each of its potential agonists. Thus we propose that a T cell can specifically increase its functional avidity for one agonist, while decreasing its functional avidity for other potential ligands. This focussing mechanism means that TCR degeneracy is inherently dynamic, allowing each TCR clonotype to have a wide range of agonists while avoiding autorecognition. The functional diversity of the TCR repertoire would therefore be greatly augmented by coreceptor-mediated ligand focussing.

Stochasticity and spatial heterogeneity in T-cell activation

Stochastic and spatial aspects are becoming increasingly recognized as an important factor in T-cell activation. Activation occurs in an intrinsically noisy environment, requiring only a handful of agonist peptide-major histocompatibility complex molecules, thus making consideration of signal to noise of prime importance in understanding sensitivity and specificity. Furthermore, it is widely established that surface-bound ligands are more effective at activation than soluble forms, while surface patternation has highlighted the role of spatial relocation in activation. Here we consider the results of a number of models of T-cell activation, from a realistic model of kinetic segregation-induced T-cell receptor (TCR) triggering through to simple queuing theory models. These studies highlight the constraints on cell activation by a surface receptor that recruits kinases. Our analysis shows that TCR triggering based on trapping of bound TCRs in regions of close proximity that exclude large ectodomain-containing molecules, such as the phosphatases CD45 and CD148, can effectively reproduce known signaling characteristics and is a viable 'signal transduction' mechanism distinct from oligomerization and conformation-based mechanisms. A queuing theory analysis shows the interrelation between sensitivity and specificity, emphasizing that these are properties of individual cell functions and need not be, nor are likely to be, uniform across different functions. In fact, threshold-based mechanisms of detection are shown to be poor at ligand discrimination because, although they can be highly specific, that specificity is limited to a small range of peptide densities. Time integration mechanisms however are able to control noise effectively, while kinetic proofreading mechanisms endow them with good specificity properties. Thus, threshold mechanisms are likely to be important for rapidly detecting minimal signaling requirements, thus achieving efficient scanning of antigen-presenting cells. However, for good specificity, time integration on a scale of hours is required.

Ligand detection and discrimination by spatial relocalization: A kinase-phosphatase segregation model of TCR activation

We develop a model of tyrosine phosphorylation and activation of the T-cell receptor (TCR) by localization to regions of close membrane-membrane proximity (close contact) that physically exclude tyrosine phosphatases such as CD45. Phosphatase exclusion generates regions of low phosphatase and high kinase activity and thus our model provides a framework to examine the kinetic segregation model of TCR activation. We incorporate a sequence of activation steps modeling the construction of the signalosome with a final sequestered, or high-stability, signaling state. The residence time of unbound TCRs in tyrosine kinase-rich domains is shown to be too short for accumulation of activation steps, whereas binding to an agonist lengthens the localization time and leads to generation of fully active TCRs. Agonist detection depends only on this localization, and therefore kinetic segregation represents a viable ligand detection mechanism, or signal transduction mechanism across membranes, distinct from receptor oligomerization and conformational change. We examine the degree of discrimination of agonists from a background of null (self) peptides, and from weak agonists achievable by this mechanism.