A role for rebinding in rapid and reliable T cell responses to antigen

Physical extraction of antigen and information

To respond and adapt, cells use surface receptors to sense environmental cues. While biochemical signal processing inside the cell is studied in depth, less is known about how physical processes during cell-cell contact impact signal acquisition. New experiments found that fast-evolving immune B cells in germinal centers (GCs) apply force to acquire antigen clusters prior to internalization, suggesting adaptive benefits of physical information extraction. We present a theory of stochastic antigen transfer and show that maximizing information gain via physical extraction can explain the dramatic phenotypic transition from naive to GC B cells-attenuated receptor signaling, enhanced force usage, and decentralized contact architecture. Our model suggests that binding-lifetime measurement and physical extraction serve as complementary modes of antigen recognition, greatly extending the dynamic range of affinity discrimination when combined. This physical-information framework further predicts that the optimal size of receptor clusters decreases as affinity improves, rationalizing the use of a multifocal synaptic pattern seen in GC B cells. By linking extraction dynamics to selection fidelity via discriminatory performance, we propose that cells may physically enhance information acquisition to sustain adaptive evolution.

Mathematical models of TCR initial triggering

T cell receptors (TCRs) play crucial roles in regulating T cell response by rapidly and accurately recognizing foreign and non-self antigens. The process involves multiple molecules and regulatory mechanisms, forming a complex network to achieve effective antigen recognition. Mathematical modeling techniques can help unravel the intricate network of TCR signaling and identify key regulators that govern it. In this review, we introduce and briefly discuss relevant mathematical models of TCR initial triggering, with a focus on kinetic proofreading (KPR) models with different modified structures. We compare the topology structures, biological hypotheses, parameter choices, and simulation performance of each model, and summarize the advantages and limitations of them. Further studies on TCR modeling design, aiming for an optimized balance of specificity and sensitivity, are expected to contribute to the development of new therapeutic strategies.

Design of Crosslinking Antibodies For T-Cell Activation: Experimental and Computational Analysis of PD-1/CD137 Bispecific Agents

Bispecific and multispecific agents have become increasingly utilized in cancer treatment and immunotherapy, yet their complex design parameters present a challenge in developing successful therapeutics. Bispecifics that crosslink receptors on two opposing cells can provide specific activation of a receptor only when these cells are in close spatial proximity, such as an immune cell and cancer cell in a tumor. These agents, including T cell activating bispecifics, can avoid off-tumor toxicity through activation only in the tumor microenvironment by utilizing a tumor target to cluster T-cell receptors for a selective costimulatory signal. Here, we investigate a panel of PD-1/CD137 targeted Humabody VH domains to determine the key factors for T cell activation, such as affinity, valency, expression level, domain orientation, and epitope location. Target expression is a dominant factor determining both specificity and potency of T cell activation. Given an intrinsic expression level, the affinity can be tuned to modulate the level of activation and IC50 and achieve specificity between low and high expression levels. Changing the epitope location and linker length showed minor improvements to activation at low expression levels, but increasing the valency for the target decreased activation at all expression levels. By combining non-overlapping epitopes for the target, we achieved higher receptor activation at low expression levels. A kinetic model was able to capture these trends, offering support for the mechanistic interpretation. This work provides a framework to quantify factors for T cell activation by cell-crosslinking bispecific agents and guiding principles for the design of new agents.

Bending the Rules: Amplifying PD-L1 Immunoregulatory Function Through Flexible Polyethylene Glycol Synthetic Linkers

Immune checkpoint signaling, such as programmed cell death protein-1 (PD-1), is a key target for immunotherapy due to its role in dampening immune responses. PD-1 signaling in T cells is regulated by complex physicochemical and mechanical cues. However, how these mechanical forces are integrated with biochemical responses remains poorly understood. Our previous work demonstrated that the use of an immobilizing polyethylene glycol (PEG) linker on synthetic microgels for the presentation of a chimeric form of PD-L1, SA-PD-L1, lead to local regulatory responses capable of abrogating allograft rejection in a model of cell-based transplantation. We herein provide evidence that enhanced immune regulating function can be obtained when presentation of SA-PD-L1 is achieved through a longer more flexible PEG chain. Presentation of SA-PD-L1 through a linker of high molecular weight, and thus longer length (10 kDa, 60 nm in length), led to enhance conversion of naive T cells into T regulatory cells (Tregs) in vitro. In addition, using a subcutaneous implant model and protein tethered through three different linker sizes (6, 30, and 60 nm) to the surface of PEG hydrogels, we demonstrated that longer linkers promoted PD-1 immunomodulatory role in vivo through three main functions: (1) augmenting immune cell recruitment at the transplant site; (2) promoting the accumulation of naive Tregs expressing migratory markers; and (3) dampening CD8+ cytolytic molecule production while augmenting expression of exhaustion phenotypes locally. Notably, accumulation of Treg cells at the implant site persisted for over 30 days postimplantation, an effect not observed when protein was presented with the shorter version of the linkers (6 and 30 nm). Collectively, these studies reveal a facile approach by which PD-L1 function can be modulated through external tuning of synthetic presenting linkers. Impact statement Recently, there has been a growing interest in immune checkpoint molecules as potential targets for tolerance induction, including programmed cell death protein-1 (PD-1). However, how the mechanics of ligand binding to PD-1 receptor affect downstream activation signaling pathways remains unresolved. By taking advantage of the effect of polyethylene glycol chain length on molecule kinetics in an aqueous solution, we herein show that PD-L1 function can be amplified by adjusting the length of the grafting linker. Our results uncover a potential facile mechanism that can be exploited to advance the role of immune checkpoint ligands, in particular PD-L1, in tolerance induction for immunosuppression-free cell-based therapies.

T-cell virtuosity in ''knowing thyself"

Major Histocompatibility Complex (MHC) I and II and the αβ T-cell antigen receptor (TCRαβ) govern fundamental traits of adaptive immunity. They form a membrane-borne ligand-receptor system weighing host proteome integrity to detect contamination by nonself proteins. MHC-I and -II exhibit the "MHC-fold", which is able to bind a large assortment of short peptides as proxies for self and nonself proteins. The ensuing varying surfaces are mandatory ligands for Ig-like TCRαβ highly mutable binding sites. Conserved molecular signatures guide TCRαβ ligand binding sites to focus on the MHC-fold (MHC-restriction) while leaving many opportunities for its most hypervariable determinants to contact the peptide. This riveting molecular strategy affords many options for binding energy compatible with specific recognition and signalling aimed to eradicated microbial pathogens and cancer cells. While the molecular foundations of αβ T-cell adaptive immunity are largely understood, uncertainty persists on how peptide-MHC binding induces the TCRαβ signals that instruct cell-fate decisions. Solving this mystery is another milestone for understanding αβ T-cells' self/nonself discrimination. Recent developments revealing the innermost links between TCRαβ structural dynamics and signalling modality should help dissipate this long-sought-after enigma.

Theoretical quantification of the polyvalent binding of nanoparticles coated with peptide-major histocompatibility complex to T cell receptor-nanoclusters

Nanoparticles (NPs) coated with peptide-major histocompatibility complexes (pMHCs) can be used as a therapy to treat autoimmune diseases. They do so by inducing the differentiation and expansion of disease-suppressing T regulatory type 1 (Tr1) cells by binding to their T cell receptors (TCRs) expressed as TCR-nanoclusters (TCR_nc). Their efficacy can be controlled by adjusting NP size and number of pMHCs coated on them (referred to as valence). The binding of these NPs to TCR_nc on T cells is thus polyvalent and occurs at three levels: the TCR-pMHC, NP-TCR_nc and T cell levels. In this study, we explore how this polyvalent interaction is manifested and examine if it can facilitate T cell activation downstream. This is done by developing a multiscale biophysical model that takes into account the three levels of interactions and the geometrical complexity of the binding. Using the model, we quantify several key parameters associated with this interaction analytically and numerically, including the insertion probability that specifies the number of remaining pMHC binding sites in the contact area between T cells and NPs, the dwell time of interaction between NPs and TCR_nc, carrying capacity of TCR_nc, the distribution of covered and bound TCRs, and cooperativity in the binding of pMHCs within the contact area. The model was fit to previously published dose-response curves of interferon-γ obtained experimentally by stimulating a population of T cells with increasing concentrations of NPs at various valences and NP sizes. Exploring the parameter space of the model revealed that for an appropriate choice of the contact area angle, the model can produce moderate jumps between dose-response curves at low valences. This suggests that the geometry and kinetics of NP binding to TCR_nc can act in synergy to facilitate T cell activation.

Understanding How Cells Probe the World: A Preliminary Step towards Modeling Cell Behavior?

Cell biologists have long aimed at quantitatively modeling cell function. Recently, the outstanding progress of high-throughput measurement methods and data processing tools has made this a realistic goal. The aim of this paper is twofold: First, to suggest that, while much progress has been done in modeling cell states and transitions, current accounts of environmental cues driving these transitions remain insufficient. There is a need to provide an integrated view of the biochemical, topographical and mechanical information processed by cells to take decisions. It might be rewarding in the near future to try to connect cell environmental cues to physiologically relevant outcomes rather than modeling relationships between these cues and internal signaling networks. The second aim of this paper is to review exogenous signals that are sensed by living cells and significantly influence fate decisions. Indeed, in addition to the composition of the surrounding medium, cells are highly sensitive to the properties of neighboring surfaces, including the spatial organization of anchored molecules and substrate mechanical and topographical properties. These properties should thus be included in models of cell behavior. It is also suggested that attempts at cell modeling could strongly benefit from two research lines: (i) trying to decipher the way cells encode the information they retrieve from environment analysis, and (ii) developing more standardized means of assessing the quality of proposed models, as was done in other research domains such as protein structure prediction.

Physical-Chemical Regulation of Membrane Receptors Dynamics in Viral Invasion and Immune Defense

Mechanical cues dynamically regulate membrane receptors functions to trigger various physiological and pathological processes from viral invasion to immune defense. These cues mainly include various types of dynamic mechanical forces and the spatial confinement of plasma membrane. However, the molecular mechanisms of how they couple with biochemical cues in regulating membrane receptors functions still remain mysterious. Here, we review recent advances in methodologies of single-molecule biomechanical techniques and in novel biomechanical regulatory mechanisms of critical ligand recognition of viral and immune receptors including SARS-CoV-2 spike protein, T cell receptor (TCR) and other co-stimulatory immune receptors. Furthermore, we provide our perspectives of the general principle of how force-dependent kinetics determine the dynamic functions of membrane receptors and of biomechanical-mechanism-driven SARS-CoV-2 neutralizing antibody design and TCR engineering for T-cell-based therapies.

NKG2D discriminates diverse ligands through selectively mechano-regulated ligand conformational changes

Stimulatory immune receptor NKG2D binds diverse ligands to elicit differential anti-tumor and anti-virus immune responses. Two conflicting degeneracy recognition models based on static crystal structures and in-solution binding affinities have been considered for almost two decades. Whether and how NKG2D recognizes and discriminates diverse ligands still remain unclear. Using live-cell-based single-molecule biomechanical assay, we characterized the in situ binding kinetics of NKG2D interacting with different ligands in the absence or presence of mechanical force. We found that mechanical force application selectively prolonged NKG2D interaction lifetimes with the ligands MICA and MICB, but not with ULBPs, and that force-strengthened binding is much more pronounced for MICA than for other ligands. We also integrated steered molecular dynamics simulations and mutagenesis to reveal force-induced rotational conformational changes of MICA, involving formation of additional hydrogen bonds on its binding interface with NKG2D, impeding MICA dissociation under force. We further provided a kinetic triggering model to reveal that force-dependent affinity determines NKG2D ligand discrimination and its downstream NK cell activation. Together, our results demonstrate that NKG2D has a discrimination power to recognize different ligands, which depends on selective mechanical force-induced ligand conformational changes.

Dephosphorylation accelerates the dissociation of ZAP70 from the T cell receptor

Protein-protein binding domains are critical in signaling networks. Src homology 2 (SH2) domains are binding domains that interact with sequences containing phosphorylated tyrosines. A subset of SH2 domain-containing proteins has tandem domains, which are thought to enhance binding affinity and specificity. However, a trade-off exists between long-lived binding and the ability to rapidly reverse signaling, which is a critical requirement of noise-filtering mechanisms such as kinetic proofreading. Here, we use modeling to show that the unbinding rate of tandem, but not single, SH2 domains can be accelerated by phosphatases. Using surface plasmon resonance, we show that the phosphatase CD45 can accelerate the unbinding rate of zeta chain-associated protein kinase 70 (ZAP70), a tandem SH2 domain-containing kinase, from biphosphorylated peptides from the T cell receptor (TCR). An important functional prediction of accelerated unbinding is that the intracellular ZAP70-TCR half-life in T cells will not be fixed but rather, dependent on the extracellular TCR-antigen half-life, and we show that this is the case in both cell lines and primary T cells. The work highlights that tandem SH2 domains can break the trade-off between signal fidelity (requiring long half-life) and signal reversibility (requiring short half-life), which is a key requirement for T cell antigen discrimination mediated by kinetic proofreading.

Influence of molecular rebinding on the reaction rate of complex formation

We simulated Brownian diffusion and reaction-diffusion processes to study the influence of molecular rebinding on the reaction rates of bimolecular reactions. We found that the number of rebinding events, N_reb, is proportional to the target's size and inversely proportional to the diffusion coefficient D and simulation time-step Δt. We found the proportionality constant close to π^-1/2. We confirmed that N_reb is defined as a ratio of the activation-limited rate constant k_a to the diffusion-limited rate constant, k_D. We provide the formula describing the reactivity coefficient κ, modelling the transient-native complex transition for the activation-controlled reaction rates. We show that κ is proportional to (D/Δt)^1/2. Finally, we apply our rebinding-including reaction rate model to the real reactions of photoacid dissociation and protein association. Based on literature data for both types of reactions, we found the Δt time-scale. We show that for the photodissociation of a proton, the Δt is equal to 171 ± 18 fs and the average number of rebinding events is approximately equal to 40. For proteins, Δt is of the order of 100 ps with around 20 rebinding events. In both cases the timescale is similar to the timescale of fluctuation of the solvent molecules surrounding the reactants; vibrations and bending in the case of photoacid dissociation and diffusional motion for proteins.

How the T cell signaling network processes information to discriminate between self and agonist ligands

T cells exhibit remarkable sensitivity and selectivity in detecting and responding to agonist peptides (p) bound to MHC molecules in a sea of self pMHC molecules. Despite much work, understanding of the underlying mechanisms of distinguishing such ligands remains incomplete. Here, we quantify T cell discriminatory capacity using channel capacity, a direct measure of the signaling network's ability to discriminate between antigen-presenting cells (APCs) displaying either self ligands or a mixture of self and agonist ligands. This metric shows how differences in information content between these two types of peptidomes are decoded by the topology and rates of kinetic proofreading signaling steps inside T cells. Using channel capacity, we constructed numerically substantiated hypotheses to explain the discriminatory role of a recently identified slow LAT Y132 phosphorylation step. Our results revealed that in addition to the number and kinetics of sequential signaling steps, a key determinant of discriminatory capability is spatial localization of a minimum number of these steps to the engaged TCR. Biochemical and imaging experiments support these findings. Our results also reveal the discriminatory role of early negative feedback and necessary amplification conferred by late positive feedback.

Stimulation strength controls the rate of initiation but not the molecular organisation of TCR-induced signalling

Millions of naïve T cells with different TCRs may interact with a peptide-MHC ligand, but very few will activate. Remarkably, this fine control is orchestrated using a limited set of intracellular machinery. It remains unclear whether changes in stimulation strength alter the programme of signalling events leading to T cell activation. Using mass cytometry to simultaneously measure multiple signalling pathways during activation of murine CD8+ T cells, we found a programme of distal signalling events that is shared, regardless of the strength of TCR stimulation. Moreover, the relationship between transcription of early response genes Nr4a1 and Irf8 and activation of the ribosomal protein S6 is also conserved across stimuli. Instead, we found that stimulation strength dictates the rate with which cells initiate signalling through this network. These data suggest that TCR-induced signalling results in a coordinated activation program, modulated in rate but not organization by stimulation strength.

Multisite reversible association in membranes and solutions: From non-Markovian to Markovian kinetics

The role of diffusion on the kinetics of reversible association to a macromolecule with two inequivalent sites is studied. Previously, we found that, in the simplest possible description, it is not sufficient to just renormalize the rate constants of chemical kinetics, but one must introduce direct transitions between the bound states in the kinetic scheme. The physical reason for this is that a molecule that just dissociated from one site can directly rebind to the other rather than diffuse away into the bulk. Such a simple description is not valid in two dimensions because reactants can never diffuse away into the bulk. In this work, we consider a variety of more sophisticated implementations of our recent general theory that are valid in both two and three dimensions. We compare the predicted time dependence of the concentrations for a wide range of parameters and establish the range of validity of various levels of the general theory.

Multiple actin networks coordinate mechanotransduction at the immunological synapse

Activation of naive T cells by antigen-presenting cells (APCs) is an essential step in mounting an adaptive immune response. It is known that antigen recognition and T cell receptor (TCR) signaling depend on forces applied by the T cell actin cytoskeleton, but until recently, the underlying mechanisms have been poorly defined. Here, we review recent advances in the field, which show that specific actin-dependent structures contribute to the process in distinct ways. In essence, T cell priming involves a tug-of-war between the cytoskeletons of the T cell and the APC, where the actin cytoskeleton serves as a mechanical intermediate that integrates force-dependent signals. We consider each of the relevant actin-rich T cell structures separately and address how they work together at the topologically and temporally complex cell-cell interface. In addition, we address how this mechanobiology can be incorporated into canonical immunological models to improve how these models explain T cell sensitivity and antigenic specificity.

Mechanosensing through immunoreceptors

The immune response is orchestrated by a variety of immune cells. The function of each cell is determined by the collective signals from various immunoreceptors, whose expression and activity depend on the developmental stages of the cell and its environmental context. Recent studies have highlighted the presence of mechanical force on several immunoreceptor-ligand pairs and the important role of force in regulating their interaction and function. In this Perspective, we use the T cell antigen receptor as an example with which to review the current understanding of the mechanosensing properties of immunoreceptors. We discuss the types of forces that immunoreceptors may encounter and the effects of force on ligand bonding, conformational change and the triggering of immunoreceptors, as well as the effects of force on the downstream signal transduction, cell-fate decisions and effector function of immune cells.

A mathematical model of combined CD8 T cell costimulation by 4-1BB (CD137) and OX40 (CD134) receptors

Combined agonist stimulation of the TNFR costimulatory receptors 4-1BB (CD137) and OX40(CD134) has been shown to generate supereffector CD8 T cells that clonally expand to greater levels, survive longer, and produce a greater quantity of cytokines compared to T cells stimulated with an agonist of either costimulatory receptor individually. In order to understand the mechanisms for this effect, we have created a mathematical model for the activation of the CD8 T cell intracellular signaling network by mono- or dual-costimulation. We show that supereffector status is generated via downstream interacting pathways that are activated upon engagement of both receptors, and in silico simulations of the model are supported by published experimental results. The model can thus be used to identify critical molecular targets of T cell dual-costimulation in the context of cancer immunotherapy.

Molecular mechanisms of T cell sensitivity to antigen

T cells initiate and regulate adaptive immune responses that can clear infections. To do this, they use their T cell receptors (TCRs) to continually scan the surfaces of other cells for cognate peptide antigens presented on major histocompatibility complexes (pMHCs). Experimental work has established that as few 1-10 pMHCs are sufficient to activate T cells. This sensitivity is remarkable in light of a number of factors, including the observation that the TCR and pMHC are short molecules relative to highly abundant long surface molecules, such as CD45, that can hinder initial binding, and moreover, the TCR/pMHC interaction is of weak affinity with solution lifetimes of approximately 1 second. Here, we review experimental and mathematical work that has contributed to uncovering molecular mechanisms of T cell sensitivity. We organize the mechanisms by where they act in the pathway to activate T cells, namely mechanisms that (a) promote TCR/pMHC binding, (b) induce rapid TCR signaling, and (c) amplify TCR signaling. We discuss work showing that high sensitivity reduces antigen specificity unless molecular feedbacks are invoked. We conclude by summarizing a number of open questions.

Mechano-regulation of Peptide-MHC Class I Conformations Determines TCR Antigen Recognition

TCRs recognize cognate pMHCs to initiate T cell signaling and adaptive immunity. Mechanical force strengthens TCR-pMHC interactions to elicit agonist-specific catch bonds to trigger TCR signaling, but the underlying dynamic structural mechanism is unclear. We combined steered molecular dynamics (SMD) simulation, single-molecule biophysical approaches, and functional assays to collectively demonstrate that mechanical force induces conformational changes in pMHCs to enhance pre-existing contacts and activates new interactions at the TCR-pMHC binding interface to resist bond dissociation under force, resulting in TCR-pMHC catch bonds and T cell activation. Intriguingly, cancer-associated somatic mutations in HLA-A2 that may restrict these conformational changes suppressed TCR-pMHC catch bonds. Structural analysis also indicated that HLA polymorphism might alter the equilibrium of these conformational changes. Our findings not only reveal critical roles of force-induced conformational changes in pMHCs for activating TCR-pMHC catch bonds but also have implications for T cell-based immunotherapy.

Identifying feasible operating regimes for early T-cell recognition: The speed, energy, accuracy trade-off in kinetic proofreading and adaptive sorting

In the immune system, T cells can quickly discriminate between foreign and self ligands with high accuracy. There is evidence that T-cells achieve this remarkable performance utilizing a network architecture based on a generalization of kinetic proofreading (KPR). KPR-based mechanisms actively consume energy to increase the specificity beyond what is possible in equilibrium. An important theoretical question that arises is to understand the trade-offs and fundamental limits on accuracy, speed, and dissipation (energy consumption) in KPR and its generalization. Here, we revisit this question through numerical simulations where we simultaneously measure the speed, accuracy, and energy consumption of the KPR and adaptive sorting networks for different parameter choices. Our simulations highlight the existence of a "feasible operating regime" in the speed-energy-accuracy plane where T-cells can quickly differentiate between foreign and self ligands at reasonable energy expenditure. We give general arguments for why we expect this feasible operating regime to be a generic property of all KPR-based biochemical networks and discuss implications for our understanding of the T cell receptor circuit.

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

Receptor-mediated cell mechanosensing

Mechanosensing depicts the ability of a cell to sense mechanical cues, which under some circumstances is mediated by the surface receptors. In this review, a four-step model is described for receptor-mediated mechanosensing. Platelet GPIb, T-cell receptor, and integrins are used as examples to illustrate the key concepts and players in this process.

Mechanosensing describes the ability of a cell to sense mechanical cues of its microenvironment, including not only all components of force, stress, and strain but also substrate rigidity, topology, and adhesiveness. This ability is crucial for the cell to respond to the surrounding mechanical cues and adapt to the changing environment. Examples of responses and adaptation include (de)activation, proliferation/apoptosis, and (de)differentiation. Receptor-mediated cell mechanosensing is a multistep process that is initiated by binding of cell surface receptors to their ligands on the extracellular matrix or the surface of adjacent cells. Mechanical cues are presented by the ligand and received by the receptor at the binding interface; but their transmission over space and time and their conversion into biochemical signals may involve other domains and additional molecules. In this review, a four-step model is described for the receptor-mediated cell mechanosensing process. Platelet glycoprotein Ib, T-cell receptor, and integrins are used as examples to illustrate the key concepts and players in this process.

Multisite Phosphorylation Modulates the T Cell Receptor ζ-Chain Potency but not the Switchlike Response

Multisite phosphorylation is ubiquitous in cellular signaling and is thought to provide signaling proteins with additional regulatory mechanisms. Indeed, mathematical models have revealed a large number of mechanisms by which multisite phosphorylation can produce switchlike responses. The T cell antigen receptor (TCR) is a multisubunit receptor on the surface of T cells that is a prototypical multisite substrate as it contains 20 sites that are distributed on 10 conserved immunoreceptor tyrosine-based activation motifs (ITAMs). The TCR ζ-chain is a homodimer subunit that contains six ITAMs (12 sites) and exhibits a number of properties that are predicted to be sufficient for a switchlike response. We have used cellular reconstitution to systematically study multisite phosphorylation of the TCR ζ-chain. We find that multisite phosphorylation proceeds by a nonsequential random mechanism, and find no evidence that multiple ITAMs modulate a switchlike response but do find that they alter receptor potency and maximum phosphorylation. Modulation of receptor potency can be explained by a reduction in molecular entropy of the disordered ζ-chain upon phosphorylation. We further find that the tyrosine kinase ZAP-70 increases receptor potency but does not modulate the switchlike response. In contrast to other multisite proteins, where phosphorylations act in strong concert to modulate protein function, we suggest that the multiple ITAMs on the TCR function mainly to amplify subsequent signaling.

Phenotypic spandrel: absolute discrimination and ligand antagonism

We consider the general problem of sensitive and specific discrimination between biochemical species. An important instance is immune discrimination between self and not-self, where it is also observed experimentally that ligands just below the discrimination threshold negatively impact response, a phenomenon called antagonism. We characterize mathematically the generic properties of such discrimination, first relating it to biochemical adaptation. Then, based on basic biochemical rules, we establish that, surprisingly, antagonism is a generic consequence of any strictly specific discrimination made independently from ligand concentration. Thus antagonism constitutes a 'phenotypic spandrel': a phenotype existing as a necessary by-product of another phenotype. We exhibit a simple analytic model of discrimination displaying antagonism, where antagonism strength is linear in distance from the detection threshold. This contrasts with traditional proofreading based models where antagonism vanishes far from threshold and thus displays an inverted hierarchy of antagonism compared to simpler models. The phenotypic spandrel studied here is expected to structure many decision pathways such as immune detection mediated by TCRs and FCϵRIs, as well as endocrine signalling/disruption.

TCR/pMHC Interaction: Phenotypic Model for an Unsolved Enigma

TCR-pMHC interaction is the keystone of the adaptive immune response. This process exhibits an impressive capacity of speed, sensitivity, and discrimination that allows detecting foreign pMHCs at very low concentration among much more abundant self-pMHC ligands. However, and despite over three decades of intensive research, the mechanisms by which this remarkable discrimination and sensitivity is attained remain controversial. In kinetic proofreading mechanisms (KPR), an increase of specificity occurs by reducing the sensitivity. To overcome this difficulty, more elaborate models including feedback processes or induced rebinding have been incorporated into the KPR scheme. Here a new approach based on the assumption that the proofreading chain behaves differently for foreign- and self-pMHC complexes has been integrated into a phenotypic model in which the complexes responsible for T cell activation stabilize (for foreign peptides) or weaken (for foreign peptides), resulting in a dramatic increase in sensitivity and specificity. Stabilization and destabilization of complexes may be caused by conformational changes, rebinding, or any other process leading to variations in the dissociation rate constants of the complexes transmitting the activation. The numerical solution and the analytical expression for the steady-state response as a function of k_off(i) (i = 0, 1, …, N, where C₀, C₁, …, C_N are the complexes in the proofreading chain) are provided. The activation chain speeds up, and larger increases in sensitivity and discrimination are obtained if the rate of activation along the proofreading chain increases for foreign pMHCs and decreases for self-ligands. Experimental implications and comparison with current models are discussed.

Mathematics in modern immunology

Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered.

First-Passage Time to Clear the Way for Receptor-Ligand Binding in a Crowded Environment

Certain biological reactions, such as receptor-ligand binding at cell-cell interfaces and macromolecules binding to biopolymers, require many smaller molecules crowding a reaction site to be cleared. Examples include the T-cell interface, a key player in immunological information processing. Diffusion sets a limit for such cavitation to occur spontaneously, thereby defining a time scale below which active mechanisms must take over. We consider N independent diffusing particles in a closed domain, containing a subregion with N_{0} particles, on average. We investigate the time until the subregion is empty, allowing a subsequent reaction to proceed. The first-passage time is computed using an efficient exact simulation algorithm and an asymptotic approximation in the limit that cavitation is rare. In this limit, we find that the mean first-passage time is subexponential, T∝e^{N_{0}}/N_{0}^{2}. For the case of T-cell receptors, we find that stochastic cavitation is exceedingly slow, 10^{9}  s at physiological densities; however, it can be accelerated to occur within 5 s with only a fourfold dilution.

Action and Traction: Cytoskeletal Control of Receptor Triggering at the Immunological Synapse

It is well known that F-actin dynamics drive the micron-scale cell shape changes required for migration and immunological synapse (IS) formation. In addition, recent evidence points to a more intimate role for the actin cytoskeleton in promoting T cell activation. Mechanotransduction, the conversion of mechanical input into intracellular biochemical changes, is thought to play a critical role in several aspects of immunoreceptor triggering and downstream signal transduction. Multiple molecules associated with signaling events at the IS have been shown to respond to physical force, including the TCR, costimulatory molecules, adhesion molecules, and several downstream adapters. In at least some cases, it is clear that the relevant forces are exerted by dynamics of the T cell actomyosin cytoskeleton. Interestingly, there is evidence that the cytoskeleton of the antigen-presenting cell also plays an active role in T cell activation, by countering the molecular forces exerted by the T cell at the IS. Since actin polymerization is itself driven by TCR and costimulatory signaling pathways, a complex relationship exists between actin dynamics and receptor activation. This review will focus on recent advances in our understanding of the mechanosensitive aspects of T cell activation, paying specific attention to how F-actin-directed forces applied from both sides of the IS fit into current models of receptor triggering and activation.

Early T cell activation: integrating biochemical, structural, and biophysical cues

T cells carry out the formidable task of identifying small numbers of foreign antigenic peptides rapidly and specifically against a very noisy environmental background of endogenous self-peptides. Early steps in T cell activation have thus fascinated biologists and are among the best-studied models of cell stimulation. This remarkable process, critical in adaptive immune responses, approaches and even seems to exceed the limitations set by the physical laws ruling molecular behavior. Despite the enormous amount of information concerning the nature of molecules involved in the T cell antigen receptor (TCR) signal transduction network, and the description of the nanoscale organization and real-time analysis of T cell responses, the general principles of information gathering and processing remain incompletely understood. Here we review currently accepted key data on TCR function, discuss the limitations of current research strategies, and suggest a novel model of TCR triggering and a few promising ways of going further into the integration of available data.

T lymphocytes need less than 3 min to discriminate between peptide MHCs with similar TCR-binding parameters

T lymphocytes need to detect rare cognate foreign peptides among numerous foreign and self-peptides. This discrimination seems to be based on the kinetics of TCRs binding to their peptide-MHC (pMHC) ligands, but there is little direct information on the minimum time required for processing elementary signaling events and deciding to initiate activation. Here, we used interference reflection microscopy to study the early interaction between transfected human Jurkat T cells expressing the 1G4 TCR and surfaces coated with five different pMHC ligands of 1G4. The pMHC concentration required for inducing 50% maximal IFN-γ production by T cells, and 1G4-pMHC dissociation rates measured in soluble phase or on surface-bound molecules, displayed six- to sevenfold variation among pMHCs. When T cells were dropped onto pMHC-coated surfaces, rapid spreading occurred after a 2-min lag. The initial spreading rate measured during the first 45 s, and the contact area, were strongly dependent on the encountered TCR ligand. However, the lag duration did not significantly depend on encountered ligand. In addition, spreading appeared to be an all-or-none process, and the fraction of spreading cells was tightly correlated to the spreading rate and spreading area. Thus, T cells can discriminate between fairly similar TCR ligands within 2 min.

The cellular environment regulates in situ kinetics of T-cell receptor interaction with peptide major histocompatibility complex

T cells recognize antigens at the two-dimensional (2D) interface with antigen-presenting cells (APCs), which trigger T-cell effector functions. T-cell functional outcomes correlate with 2D kinetics of membrane-embedded T-cell receptors (TCRs) binding to surface-tethered peptide-major histocompatibility complex molecules (pMHCs). However, most studies have measured TCR-pMHC kinetics for recombinant TCRs in 3D by surface plasmon resonance, which differs drastically from 2D measurements. Here, we compared pMHC dissociation from native TCR on the T-cell surface to recombinant TCR immobilized on glass surface or in solution. Force on TCR-pMHC bonds regulated their lifetimes differently for native than recombinant TCRs. Perturbing the cellular environment suppressed 2D on-rates but had no effect on 2D off-rate regardless of whether force was applied. In contrast, for the TCR interacting with its monoclonal antibody, the 2D on-rate was insensitive to cellular perturbations and the force-dependent off-rates were indistinguishable for native and recombinant TCRs. These data present novel features of TCR-pMHC kinetics that are regulated by the cellular environment, underscoring the limitations of 3D kinetics in predicting T-cell functions and calling for further elucidation of the underlying molecular and cellular mechanisms that regulate 2D kinetics in physiological settings.

Linking form to function: Biophysical aspects of artificial antigen presenting cell design

Artificial antigen presenting cells (aAPCs) are engineered platforms for T cell activation and expansion, synthesized by coupling T cell activating proteins to the surface of cell lines or biocompatible particles. They can serve both as model systems to study the basic aspects of T cell signaling and translationally as novel approaches for either active or adoptive immunotherapy. Historically, these reductionist systems have not been designed to mimic the temporally and spatially complex interactions observed during endogenous T cell-APC contact, which include receptor organization at both micro- and nanoscales and dynamic changes in cell and membrane morphologies. Here, we review how particle size and shape, as well as heterogenous distribution of T cell activating proteins on the particle surface, are critical aspects of aAPC design. In doing so, we demonstrate how insights derived from endogenous T cell activation can be applied to optimize aAPC, and in turn how aAPC platforms can be used to better understand endogenous T cell stimulation. This article is part of a Special Issue entitled: Nanoscale membrane organisation and signalling.

Accumulation of dynamic catch bonds between TCR and agonist peptide-MHC triggers T cell signaling

TCR-pMHC interactions initiate adaptive immune responses, but the mechanism of how such interactions under force induce T cell signaling is unclear. We show that force prolongs lifetimes of single TCR-pMHC bonds for agonists (catch bonds) but shortens those for antagonists (slip bonds). Both magnitude and duration of force are important, as the highest Ca(2+) responses were induced by 10 pN via both pMHC catch bonds whose lifetime peaks at this force and anti-TCR slip bonds whose maximum lifetime occurs at 0 pN. High Ca(2+) levels require early and rapid accumulation of bond lifetimes, whereas short-lived bonds that slow early accumulation of lifetimes correspond to low Ca(2+) responses. Our data support a model in which force on the TCR induces signaling events depending on its magnitude, duration, frequency, and timing, such that agonists form catch bonds that trigger the T cell digitally, whereas antagonists form slip bonds that fail to activate.

Accumulation of serial forces on TCR and CD8 frequently applied by agonist antigenic peptides embedded in MHC molecules triggers calcium in T cells

T cell activation by Ag is one of the key events in adaptive immunity. It is triggered by interactions of the TCR and coreceptor (CD8 or CD4) with antigenic peptides embedded in MHC (pMHC) molecules expressed on APCs. The mechanism of how signal is initiated remains unclear. In this article, we complement our two-dimensional kinetic analysis of TCR-pMHC-CD8 interaction with concurrent calcium imaging to examine how ligand engagement of TCR with and without the coengagement of CD8 initiates signaling. We found that accumulation of frequently applied forces on the TCR via agonist pMHC triggered calcium, which was further enhanced by CD8 cooperative binding. Prolonging the intermission between sequential force applications impaired calcium signals. Our data support a model where rapid accumulation of serial forces on TCR-pMHC-CD8 bonds triggers calcium in T cells.

Mechanical regulation of T-cell functions

T cells are key players of the mammalian adaptive immune system. They experience different mechanical microenvironments during their life cycle, from the thymus, secondary lymph organs, and peripheral tissues that are free of externally applied force, but display variable substrate rigidities to the blood and lymphatic circulation systems, where complicated hydrodynamic forces are present. Regardless of whether T cells are subject to external forces or generate their own internal forces, they respond and adapt to different biomechanical cues to modulate their adhesion, migration, trafficking, and triggering of immune functions through mechanical regulation of various molecules that bear force. These include adhesive receptors, immunoreceptors, motor proteins, cytoskeletal proteins, and their associated molecules. Here, we discuss the forces acting on various surface and cytoplasmic proteins of a T cell in different mechanical milieus. We review existing data on how force regulates protein conformational changes and interactions with counter molecules, including integrins, actin, and the T-cell receptor, and how each relates to T-cell functions.

Receptor Pre-Clustering and T cell Responses: Insights into Molecular Mechanisms

T cell activation, initiated by T cell receptor (TCR) mediated recognition of pathogen-derived peptides presented by major histocompatibility complex class I or II molecules (pMHC), shows exquisite specificity and sensitivity, even though the TCR-pMHC binding interaction is of low affinity. Recent experimental work suggests that TCR pre-clustering may be a mechanism via which T cells can achieve such high sensitivity. The unresolved stoichiometry of the TCR makes TCR-pMHC binding and TCR triggering, an open question. We formulate a mathematical model to characterize the pre-clustering of T cell receptors (TCRs) on the surface of T cells, motivated by the experimentally observed distribution of TCR clusters on the surface of naive and memory T cells. We extend a recently introduced stochastic criterion to compute the timescales of T cell responses, assuming that ligand-induced cross-linked TCR is the minimum signaling unit. We derive an approximate formula for the mean time to signal initiation. Our results show that pre-clustering reduces the mean activation time. However, additional mechanisms favoring the existence of clusters are required to explain the difference between naive and memory T cell responses. We discuss the biological implications of our results, and both the compatibility and complementarity of our approach with other existing mathematical models.

An induced rebinding model of antigen discrimination

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We propose that pMHC binding to TCR can increase (induce) pMHC rebinding.

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Published studies are consistent with an induced rebinding model.

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Induced rebinding improves the ability of T cells to discriminate antigens.

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Induced rebinding relates 3D to 2D TCR–pMHC binding parameters.

T cells have to detect rare high-affinity ‘foreign’ peptide MHC (pMHC) ligands among abundant low-affinity ‘self’-peptide MHC ligands. It remains unclear how this remarkable discrimination is achieved. Kinetic proofreading mechanisms can provide the required specificity but only at the expense of much reduced sensitivity. A number of recent observations suggest that pMHC engagement of T cell receptors (TCRs) induces changes such as clustering and/or conformational alterations that enhance subsequent rebinding. We show that inclusion of induced rebinding to the same pMHC in kinetic proofreading models enhances the sensitivity of TCR recognition while retaining specificity. Moreover, induced rebinding is able to reproduce the striking, and hitherto unexplained, 2D membrane-binding properties recently reported for the TCR.

Co-Receptor CD8-Mediated Modulation of T-Cell Receptor Functional Sensitivity and Epitope Recognition Degeneracy

The interaction between T-cell receptors (TCRs) and peptide epitopes is highly degenerate: a TCR is capable of interacting productively with a wide range of different peptide ligands, involving not only cross-reactivity proper (similar epitopes elicit strong responses), but also polyspecificity (ligands with distinct physicochemical properties are capable of interacting with the TCR). Degeneracy does not gainsay the fact that TCR recognition is fundamentally specific: for the vast majority of ligands, the functional sensitivity of a given TCR is virtually null whereas this TCR has an appreciable functional sensitivity only for a minute fraction of all possible ligands. Degeneracy can be described mathematically as the probability that the functional sensitivity, of a given TCR to a randomly selected ligand, exceeds a set value. Variation of this value generates a statistical distribution that characterizes TCR degeneracy. This distribution can be modeled on the basis of a Gaussian distribution for the TCR/ligand dissociation energy. The kinetics of the TCR and the MHCI molecule can be used to transform this underlying Gaussian distribution into the observed distribution of functional sensitivity values. In the present paper, the model is extended by accounting explicitly for the kinetics of the interaction between the co-receptor and the MHCI molecule. We show that T-cells can modulate the level of degeneracy by varying the density of co-receptors on the cell surface. This could allow for an analog of avidity maturation during incipient T-cell responses.

T lymphocytes sense antigens within seconds and make a decision within one minute

Adaptive immune responses are triggered by the rapid and sensitive detection of MHC-bound peptides by TCRs. The kinetics of early TCR/APC contacts are incompletely known. In this study, we used total internal reflection fluorescence microscopy to image human T cell membranes near model surfaces: contact was mediated by mobile protrusions of <0.4 μm diameter. The mean lifetime of contacts with a neutral surface was 8.6 s. Adhesive interactions increased mean contact time to 27.6 s. Additional presence of TCR ligands dramatically decreased contact to 13.7 s, thus evidencing TCR-mediated triggering of a pulling motion within seconds after ligand encounter. After an interaction typically involving 30-40 contacts formed during a 1-min observation period, TCR stimulation triggered a rapid and active cell spreading. Pulling events and cell spreading were mimicked by pharmacological phospholipase Cγ1 activation, and they were prevented by phospholipase Cγ1 inhibition. These results provide a quantitative basis for elucidating the earliest cell response to the detection of foreign Ags.

A large number of receptors may reduce cellular response time variation

Cells often have tens of thousands of receptors, even though only a few activated receptors can trigger full cellular responses. Reasons for the overabundance of receptors remain unclear. We suggest that, under certain conditions, the large number of receptors can result in a competition among receptors to be the first to activate the cell. The competition decreases the variability of the time to cellular activation, and hence results in a more synchronous activation of cells. We argue that, in simple models, this variability reduction does not necessarily interfere with the receptor specificity to ligands achieved by the kinetic proofreading mechanism. Thus cells can be activated accurately in time and specifically to certain signals. We predict the minimum number of receptors needed to reduce the coefficient of variation for the time to activation following binding of a specific ligand. Furthermore, we predict the maximum number of receptors so that the kinetic proofreading mechanism still can improve the specificity of the activation. These predictions fall in line with experimentally reported receptor numbers for multiple systems.

The interdisciplinary science of T-cell recognition

The recognition of peptide/MHC antigens by T-cells has continued to challenge the imagination of immunologists, biochemists, and cell biologists alike. This is at least in part because T-cell recognition connects a diversity of issues and transcends many scientific disciplines. A fundamental unsolved issue is how T-cells manage to detect even a single molecule of an agonist pMHC complex, which is vastly outnumbered by endogenous pMHCs, many of which involve the same MHC molecule. They do so although TCRs are cross-reactive and typically low in affinity when measured in isolation. Importantly, T-cell antigen recognition takes place within the contact zone between a T-cell and the antigen-presenting cell, termed the immunological synapse. This bimembrane structure sets the stage for the antigen-binding events and all subsequent molecular recognition events. There is increasing evidence that the molecular dynamics of receptor-ligand interactions are not only dependent on the intrinsic properties of the binding partners but also become transformed by cell biological parameters such as the geometrical constraints within the immune synapse, mechanical forces, and local molecular crowding. To appreciate the complete picture, we think a multidisciplinary approach is imperative, which includes genetics, biochemistry, and structure determination and also biophysical analyses and the latest molecular imaging techniques. Here, we review earlier pioneering work and also recent developments in the fascinating and interdisciplinary science of T-cell antigen recognition. In many ways, this work may present a useful "roadmap" for work in other systems of cell-cell recognition, which underlie many fundamental biological phenomenons of interest.

Non-catalytic tyrosine-phosphorylated receptors

Leukocytes play a critical role in recognizing and responding to infection and cancer. Central to this function is an array of cell-surface receptors that lack sequence homology. Many of these receptors have in common the fact that their signaling involves phosphorylation of cytoplasmic domains by extrinsic tyrosine kinases. These non-catalytic tyrosine-phosphorylated receptors (NTRs) share a number of other features, including small size and optimal stimulation by surface-associated ligands. We argue here that NTRs are also likely to share the same kinetic-segregation triggering mechanism, which involves segregation of the engaged NTR from receptor tyrosine phosphatases with large ectodomains such as CD45 and CD148. NTRs signal through tyrosine-containing cytoplasmic motifs, which recruit distinct cytoplasmic signaling proteins when phosphorylated, transducing activatory or inhibitory signals. They have two features that make them uniquely well suited to their role in immune recognition of infection and cancer. Their modular structure enables the coupling of many rapidly evolving receptors with diverse ligand specificities to the same conserved signaling machinery. Their similarity in size and shared signaling machinery enables them to colocalize at cell-cell interfaces when they engage ligands, facilitating the integration of activatory and inhibitory signals from multiple receptors at the cell surface.

Protein clusters on the T cell surface may suppress spurious early signaling events

T cells play an important role in the adaptive immune system, quickly activating effector functions in response to small numbers of antigenic peptides but rarely activating in response to constant interaction with most endogenous peptides. Emerging experimental evidence suggests that key membrane-bound signaling proteins such as the T cell receptor and the adaptor protein Lat are spatially organized into small clusters on the T cell membrane. We use spatially resolved, stochastic computer simulations to study how the inhomogeneous distribution of molecules affects the portion of the T cell signaling network in which the kinase ZAP-70, originating in T cell receptor clusters, phosphorylates Lat. To gain insight into the effects of protein clustering, we compare the signaling response from membranes with clustered proteins to the signaling response from membranes with homogeneously distributed proteins. Given a fixed amount of ZAP-70 (a proxy for degree of TCR stimulation) that must diffuse into contact with Lat molecules, the spatially homogeneous system responds faster and results in higher levels of phosphorylated Lat. Analysis of the spatial distribution of proteins demonstrates that, in the homogeneous system, nearest ZAP-70 and Lat proteins are closer on average and fewer Lat molecules share the same closest ZAP-70 molecule, leading to the faster response time. The results presented here suggest that spatial clustering of proteins on the T cell membrane may suppress the propagation of signal from ZAP-70 to Lat, thus providing a regulatory mechanism by which T cells suppress transient, spurious signals induced by stimulation of T cell receptors by endogenous peptides. Because this suppression of spurious signals may occur at a cost to sensitivity, we discuss recent experimental results suggesting other potential mechanisms by which ZAP-70 and Lat may interact to initiate T cell activation.

T cell triggering: insights from 2D kinetics analysis of molecular interactions

Interaction of the T cell receptor (TCR) with pathogen-derived peptide presented by the major histocompatibility complex (pMHC) molecule is central to adaptive immunity as it initiates intracellular signaling to trigger T cell response to infection. Kinetic parameters of this interaction have been under intensive investigation for more than two decades using soluble pMHCs and/or TCRs with at least one of them in the solution (three-dimensional (3D) methods). Recently, several techniques have been developed to enable kinetic analysis on live T cells with pMHCs presented by surrogate antigen presenting cells (APCs) or supported planar lipid bilayers (two-dimensional (2D) methods). Comparison of 2D versus 3D parameters reveals drastic differences with broader ranges of 2D affinities and on-rates and orders of magnitude faster 2D off-rates for functionally distinct pMHCs. Here we review new 2D data and discuss how it may impact previously developed models of T cell discrimination between pMHCs of different potencies.

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.

Systems biology in immunology: a computational modeling perspective

Systems biology is an emerging discipline that combines high-content, multiplexed measurements with informatic and computational modeling methods to better understand biological function at various scales. Here we present a detailed review of the methods used to create computational models and to conduct simulations of immune function. We provide descriptions of the key data-gathering techniques employed to generate the quantitative and qualitative data required for such modeling and simulation and summarize the progress to date in applying these tools and techniques to questions of immunological interest, including infectious disease. We include comments on what insights modeling can provide that complement information obtained from the more familiar experimental discovery methods used by most investigators and the reasons why quantitative methods are needed to eventually produce a better understanding of immune system operation in health and disease.

Spot variation fluorescence correlation spectroscopy allows for superresolution chronoscopy of confinement times in membranes

Resolving the dynamical interplay of proteins and lipids in the live-cell plasma membrane represents a central goal in current cell biology. Superresolution concepts have introduced a means of capturing spatial heterogeneity at a nanoscopic length scale. Similar concepts for detecting dynamical transitions (superresolution chronoscopy) are still lacking. Here, we show that recently introduced spot-variation fluorescence correlation spectroscopy allows for sensing transient confinement times of membrane constituents at dramatically improved resolution. Using standard diffraction-limited optics, spot-variation fluorescence correlation spectroscopy captures signatures of single retardation events far below the transit time of the tracer through the focal spot. We provide an analytical description of special cases of transient binding of a tracer to pointlike traps, or association of a tracer with nanodomains. The influence of trap mobility and the underlying binding kinetics are quantified. Experimental approaches are suggested that allow for gaining quantitative mechanistic insights into the interaction processes of membrane constituents.

Antigen potency and maximal efficacy reveal a mechanism of efficient T cell activation

T cell activation, a critical event in adaptive immune responses, depends on productive interactions between T cell receptors (TCRs) and antigens presented as peptide-bound major histocompatibility complexes (pMHCs). Activated T cells lyse infected cells, secrete cytokines, and perform other effector functions with various efficiencies, which depend on the binding parameters of the TCR-pMHC complex. The mechanism through which binding parameters are translated to the efficiency of T cell activation, however, remains controversial. The "affinity model" suggests that the dissociation constant (KD) of the TCR-pMHC complex determines the response, whereas the "productive hit rate model" suggests that the off-rate (koff) is critical. Here, we used mathematical modeling to show that antigen potency, as determined by the EC50 (half-maximal effective concentration), which is used to support KD-based models, could not discriminate between the affinity and the productive hit rate models. Both models predicted a correlation between EC50 and KD, but only the productive hit rate model predicted a correlation between maximal efficacy (Emax), the maximal T cell response induced by pMHC, and koff. We confirmed the predictions made by the productive hit rate model in experiments with cytotoxic T cell clones and a panel of pMHC variants. Thus, we propose that the activity of an antigen is determined by both its potency (EC50) and maximal efficacy (Emax).