Bispecific immune cell therapies were originally proposed by (Nisonoff and Rivers, 1961) falling within the class of immuno-oncology therapies wherein one binding domain that targets the cancer antigen and the other targets the T cell receptor (TCR). The involvement of the TCR complex facilitates the recognition, and mediates the redirected lysis, of the cancer cells by T cells. The perforin and granzymes released by the effector cells downstream of the activation of the T cells, results into the apoptosis and killing of the targeted cancer cells. Typically, TCEs are designed with low-affinity binding to the TCR, in the micromolar range, with higher affinity for the tumour-associated antigens (TAAs), in the nanomolar range. The formation of “trimers” (that is to say, a TCR-TCE-TAA trimeric synapse that cross-bridges the effector cell and the tumor cell) is widely understood to be a key driver of cytotoxic function and therefore efficacy, by forming artificial immunological synapses (Betts et al., 2019; Flowers et al., 2023). Bispecific molecules that can form ternary complexes (or trimers) are known to exhibit a bell-shaped dose-response, something that was both predicted by mathematical arguments and confirmed experimentally Douglass et al. (2013); Lin and Chen (2021); Granger et al. (2021). At this point in time, measurement of trimeric synapses in vivo is still challenging, and can only be inferred indirectly from in-vitro assays. Direct absolute quantification of this important biomarker in a clinical setting is still elusive, and that leaves mechanistic modeling as an avenue to help predict clinically efficacious doses, and minimize costly and wasteful trial-and-error at the clinical trial stage. We may speculate that in vitro trimer quantification could be obtained by fluorescence imaging methods similar to those employed in the study of other compounds whose mechanism of action relies on ternary complexes, such as PROTACs. A potential avenue could be the use of something akin to AlphaLISA or TR-FRET fluorescence essays, where the simultaneous signal of activated bound fluorophores brought into close proximity is detected, as reviewed for example in Casement et al. (2021). Alternatively, other authors have used cross-linking assays that relied on flow cytometry Qi et al. (2018). While sample collection in a clinical setting may be impossible, translatable insight could be gained by exploiting the recent progresses in the rapidly developing field of micro-physiological systems (MPS), where human-derived tissue is cultured in vitro Virumbrales-Muñoz and Ayuso (2022).

While the impact of relative affinity of TCE design has been pointed out by other authors (Vafa and Trinklein, 2020), due to the complex interactions involved in TCE with different cell types, number of receptors, binding affinity, a quantitative understanding of the interplay between these parameters is challenging. A higher affinity for the TCR would have a theoretically positive impact on trimer formation, but at the expense of increased risk of cytokine release, increased risk of T-cell exhaustion (Zhang et al., 2024) and biodistribution into lymphocyte-rich tissues at the expenses of the tumor tissue, thereby reducing local exposure (Vafa and Trinklein, 2020). However, erring on the side of caution with respect to cytokine release may lead us to select a TCR affinity too low for efficacy. Conversely, excessively high affinity for the TAA may improve trimer formation, but also increase internalisation by tumor cells and reduce local exposure by decreasing the TCE’s half-life (Mandikian et al., 2018). In the face of such non-trivial trade-offs, quantitative mathematical modeling can be helpful for guiding a rational selection of compound parameters that determine efficacy and safety.

This study is a first attempt to explore the relationship between TCE concentration and trimer formation under varying target cancer receptor expression levels. We advocate both continued development of more accurate models, and model interrogation to assist design choices. For the sake of simplicity, we are focusing on target engagement, in particular on the impact of relative affinity and local exposure on the formation of trimers, which are the fundamental driver of cytotoxic function. As a test-bench, we selected the case of a bispecific TCE targeting TAAs at baseline B-cells levels human lymph nodes, for which most relevant parameters (such as cell counts and surface receptors copy numbers) could be sourced from the literature (Ginaldi et al., 1998; Nerreter et al., 2019; Mandikian et al., 2018; Stulnig et al., 1995; Liu et al., 2000). The baseline values for TCR and TAA affinities where selected in accordance to the values recommended by Vafa and Trinklein (2020).

Models addressing specific indications, with different targets and/or different levels of disease burden, will have to rely on disease-specific biological and histological data to quantify cell counts and target expression levels.

This analysis aims to explain how factors like expression levels, the TCE binding affinity to its targets, and TCE exposure are interrelated, in particular when they are perturbed around the “classical” recommended values for TCE design. Figure 2A shows state equilibrium concentrations of dimers and trimers at varying concentrations of TCE. Figure 2B shows the relationship between predicted trimer formation and TCE concentration, given three different TAA expression level conditions. This effect may also be relevant to quantify loss of efficacy in the event of target downregulation after repeated dosing. The effect of a change of TCR affinity (Kd around the “typical” value of 1 μ M ) is illustrated in Figure 3A, while the effect of a change of affinity for TAA (Kd around the “typical” value of 1 n M ) is illustrated in Figure 3B. Given that the affinity for the TAA is already high, a further increase would not boost peak trimer formation, but rather lower the exposure at which saturation is reached, whereas increasing TCR affinity could rescue low efficacy by having a more dramatic effect on peak trimer formation. As previously mentioned, however, this must be weighed against the increased risk of cytokine release, which poses a safety concern.

A strong assumption underlying our modelling approach is that we are using TCR occupancy as a driver of efficacy. In naturally occurring immunological synapses, TCR occupancy is not sufficient for T cell activation. While TCR occupancy remains a necessary first step, co-stimulatory signals are also required. However, the synapse formed by TCEs is rather different from a physiological one. Usually the TCE targets directly a co-receptor subunit of the TCR complex, rather than the TCR central region itself. The interaction with the antigen is delegated to the second arm of the bispecific TCE, which binds directly to a surface antigen rather than an antigen peptide bound to an MHC. A salient feature of the artificial ternary synapses created by TCEs is their ability to induce cytotoxic responses independently from both MHC binding and co-stimulation (Bargou et al., 2008; Burt et al., 2019). To our knowledge, the resulting intracellular signaling is not well-mapped or quantitatively understood, but we believe it is fair to assume it is likely to differ from “standard” T-cell activation. In addition, since both in vivo and in vitro data show a clear exposure-response relationship, and since occupancy is clearly related to exposure, we decided to use occupancy as a crude but convenient proxy for what we may call “T-cell activation propensity”. Moreover, trimeric synapses have an important additional non-signalling function, namely, forcing cytotoxic T-cells to co-localize with their target cells.

A second simplifying assumption is the use of a well-mixed compartment to represent binding events. In fact, the second binding step happens between one free and one TCE-occupied receptor, floating on the membranes of two contiguous cells separated by a small gap of interstitial fluid. As pointed out by other authors, from a kinetic point of view, the net impact of membrane localization is not an obvious one, because although 2D diffusive searches are known to be more efficient than their 3D counterparts, which speeds up the reaction rate, diffusion in lipid bilayers restricts access to reactants and is orders of magnitude slower than in bulk solution, which slows down the reaction rate. Given the complexity of the problem and the current lack of specific data, we preferred to adopt the simplest possible approach, and defer a more thorough analysis to future work, possibly with agent-based models rather then ODE-based ones, as described for example by (Andrews, 2020).

Within the limitations outlined above, our results highlight a potentially critical factor involved in the design of effective TCE drugs. The optimal TCE exposure for creating the most effective trimer complexes (where the drug bridges the T-cell and cancer cell) relies mainly on the binding affinity between the TCE and the two targets: the expressed TAA on cancer cells and the T-cell receptor. Interestingly, the cancer receptor expression level in a patient does not influence the optimal TCE exposure: but it does affect the overall amount of trimer formation, it does not shift the exposure that yields the maximum trimer formation. A descriptive way of phrasing the effect of TAA expression levels is that they shift the dose-response curve “up and down” along the y-axis, but not “left and right” along the x-axis.

Since patient factors like T-cell concentration and TAA expression levels are not controllable, designing drugs with optimal target binding affinity becomes critical for clinical success. The safety requirement to minimize cytokine release risk by choosing TCEs with relatively low affinity for TCR creates an inevitable safety/efficacy trade-off that is best negotiated with the support of predictive models. This consideration should influence decisions about compound design and dosing strategies. On the other hand, selecting the right targets is essential as well. The TAA expression level directly affects the TCE exposure needed to activate enough T-cells for a potent immune response. If the TCE exposure is too low, there won’t be enough trimer formation to trigger a strong immune response. However, if the exposure is pushed beyond the ideal point, T-cell activation won’t necessarily increase due to more inactive dimer formation instead of active trimer formation–i.e., the system becomes saturated with dimers.

It is worth stressing that large molecules such as TCEs have more complex biodistribution patterns than small molecules (Xenaki et al., 2017), and local tissue exposure is most likely one of the main drivers of the target engagement mechanism that we discussed in this work. Therefore, a thorough understanding of how the drug distributes throughout the body and interacts with its targets on both cancer cells and T-cells should be prioritized from the very beginning of the design process. This knowledge will be instrumental in selecting the right binding strengths, choosing optimal targets, and ultimately, determining the most effective dosing strategies for TCE therapies.