A cell topography-based mechanism for ligand discrimination by the T cell receptor

Significance One approach to testing biological theories is to determine if they are predictive. We have developed a simple, theoretical treatment of T cell receptor (TCR) triggering that relies on just two physical principles: (i) the time TCRs spend in cell–cell contacts depleted of large tyrosine phosphatases and (ii) constraints on the size of these contacts imposed by cell topography. The theory not only distinguishes between agonistic and nonagonistic TCR ligands but predicts the relative signaling potencies of agonists with remarkable accuracy. These findings suggest that the theory captures the essential features of receptor triggering.


I. Appendix I: A quantitative treatment of TCR signaling a) Description of the rationale and the assumptions of the TCR triggering model
This model seeks to mathematically describe TCR dwell-time inside close contacts. Close contacts are defined as any area of cell contact from which CD45 is excluded, and therefore correspond to the "close contacts" first described in Chang et al. Our experiments and others show that these contacts are initially small and grow over time (see Movie S3; Chang et al., 2016, Razvag et al., 2018. Cell-cell contacts appear to be highly dynamic in the absence of signaling. Since we are interested in signal initiation, we assume that close contacts form for finite periods (referred to as the contact duration). We base our model on the kinetic-segregation (KS) model (Davis and van der Merwe, 1998;Davis et al. 2006). The KS model proposes that receptor triggering requires only that the TCR stays accessible to kinases within close contacts, protected from phosphatases that would otherwise terminate signaling, and for TCR phosphorylation to be sufficiently long-lived for downstream effects to be initiated. pMHC ligands, via trapping effects, serve only to increase the residence time of the TCR inside the close contact. We therefore assume for our modeling (1) that when a close contact is formed, TCRs can diffuse in and out of the contact, and (2) that while the TCR is bound to a ligand inside the close contact, it is unable to leave. The second assumption means that the residence time of a bound TCR is independent from its diffusion, so we do not need to account for any changes in TCR diffusion coefficients upon pMHC binding: the dwell-time of a bound TCR is solely determined by the off-rate of the complex, combined with its free diffusion before and after pMHC binding. The assumption that a pMHC/TCR pair will not leave the contact is supported by the fact that this is energetically unfavorable due to the complex's size being of the same dimensions as the spacing of the two membranes in a close contact (James and Vale, 2012). Irrespective of its binding status, any TCR that remains in the close contact for 2 seconds or longer -due to pMHC binding per se or due to diffusion, or both -is assumed to be triggered by our model. We chose tmin = 2 seconds, given that kcat(Lck) = 3.41 s -1 and that, at a CD45/Lck ratio of 2:1, ITAM phosphorylation is reduced by ~50% (Hui and Vale, 2014). We note that the regulatory phosphorylation of Lck (on Y394 and Y505 residues), also under the influence of CD45, has very little effect on kcat and is therefore unlikely to affect this parameter (i.e. unphosphorylated and doubly phosphorylated Lck have similar kcat, 3.41 versus 3.29 s -1 ). If therefore we assume an effective ITAM phosphorylation rate of kcat,eff ≈2 s -1 , this still means that in 2 seconds ~ 4 pTyr-generating events would occur, which correspond to two pTyr ITAM signaling domains. We further assume that this is sufficient to initiate downstream signaling. There is experimental evidence that TCR triggering occurs within this time-frame upon pMHC binding (2)(3)(4)(5)(6). In essence, by introducing tmin we consider a distribution of phosphorylation times with a sharp lower boundary created by the maximal turnover rate of Lck in the case of immediate substrate binding (i.e. kcat). If a TCR leaves but re-enters shortly thereafter, then that TCR's sojourn inside the close contact is considered separately with a restarted clock, assuming that triggering occurs after a TCR has occupied the close contact continuously for 2 seconds and not cumulatively over multiple excursions, since CD45 reverses any phosphorylation once the TCR leaves the close contact. The model calculates TCR density across the close contact based on the rate of TCR entry into this area (for a given contact radius, initial TCR density and TCR diffusion coefficient). Therefore, it can also account for changes in TCR entrance rate and in the dwell-time of TCRs already present inside the close contact as it grows. To achieve sufficient accuracy, the model requires moving-boundary coupled partial differential equations that are computationally expensive. While the problem is solved numerically on a disc, the solution is fully two dimensional and not radially symmetric (although the domain is). Our method of simulation is based on a finite element discretization implemented in MATLAB. b) Modelling of receptor triggering using moving-boundary coupled partial differential equations to account for close contact growth See Figs 1-5, Supplementary table 2 and Movie S1

i) Model formulation
Since close contacts (CC) grow on time-scales similar to the diffusion of the TCR, changes in TCR density in CC need to be described by a coupled system of moving-boundary partial differential equations (PDEs), ∂#/ ∂% = ' ( ∇ * # − , on * # + , off /, 0 < |r| < 4(%; % entry ); ∂// ∂% = ' 8 ∇ * / + , on * # − , off /, 0 < |r| < 4(%; % entry ), where #(:, %; % entry ) and /(:, %; % entry ) represent free and ligand-complexed TCRs diffusing with coefficient D < and D = , respectively, and with the receptors undergoing reversible binding with firstorder rates (, >? * ,k ABB ). Note that , >? * = , AC [M] where , AC is the bimolecular on-rate (in units of GH * I ⁄ ) and [M] is the ligand concentration (in units of GH K* ). We have assumed that TCRs within a CC do not compete for pMHC and this is reflected in using first-order kinetics for binding. This approximation is reasonable when the number of pMHC is larger than the number of bound TCRs at all times within the CC. The boundary conditions for the disc domain of radius 4 are adsorbing for # and no flux for /, Importantly, the domain area grows linearly in time and therefore, 4(%; % entry ) = P4 Q * + R(% + % entry )/S where R is the growth rate (in units of GH * I ⁄ ) and % is time. The initial conditions at % = % T?UVW are as follows, where r Q = (R Q − ε, θ). The additional term 4 ' (%)/ , which reflects the rate of growth in the region, is a necessary addition to the usual Neumann condition in order to prevent mass of / leaving the domain. To see this, consider the change in total mass `(%) = ∫ (# + /)  parameter ϵ is the distance from the boundary that the TCR is initialized in its exploration of the CC.
For technical reasons, the initial location cannot be exactly on the boundary as one would ideally like since the mathematical formulation of the dwell time would not be well posed. This is because a Brownian walker initially on the boundary will interact with the boundary an infinite number of times.
Therefore, we must start the particle just inside the domain and we have used a value of ϵ = 0.09 for the numerical simulations.

ii) Model output
The output of the model is the probability (j k ) that a single receptor has remained within the CC for more than 2 seconds, for contact duration (% l ), j k (% entry ) = m #(:, 2; % entry ) + /(:, 2; % entry ) b(*;U entry ) c:.
(equation 1.6) The time-dependent rate of TCR entry into the domain (, U (%)) is expected to be proportional to the size of the domain, which increases over time. Using previously derived results (see Equation 11 in Weaver, 1983), we find, where x = 415 GH * is the cell surface area, # | = 100 GH K* (varied over the simulations; see also Given that multiple receptors can enter the CC during the contact duration (% l ), we need to calculate the probability that at least one TCR has remained within the domain for more than 2 s (j | , referred to as "triggering probability"). The number of TCRs that have entered the domain in time interval [%~, %~+ Δ%] can be estimated as , U (%~)Δ% so that j | is estimated as follows, In the case where j k and , U are constants: When considering the limiting case of kt(t) = 0 for the growing CC model, we have assumed a small initial radius (0.01 µm) and therefore assumed that the CC is empty of TCRs. In cases where we do not have a growing CC (R = 0, Fig. 3C), a term is included representing the initial number of TCRs in the CC at % = 0, All plots for the theoretical modelling of TCR triggering were generated in MATLAB (MATLAB R 2014b, The MathWorks, Natick, US) using the equations derived in this section.

d) Data and code availability statement
The data sets generated during and analyzed during the current study as well as all custom-written software are available from the corresponding author on reasonable request.

Plasmids
For expressing HA-CD45-Halo, LCK-Halo, and TCRβ-Halo (New England Biolabs, UK) the genes were amplified by PCR to produce dsDNA fragments encoding the proteins of interest flanked at the 3' end by a sequence coding for a Gly-Ser linker which was followed by Halo-tag. Following confirmation of sequence and reading frame integrity the Lck-Halo and TCRβ-Halo were sub-cloned into the lentiviral pHR-SIN plasmid. To generate mmLck the appropriate residues were mutated by a PCR amplification reaction using forward and reverse oligonucleotides encoding the desired mutation.
Sequence integrity was confirmed by reversible terminator base sequencing.
(ThermoFisher) per the manufacturer's protocol. Fab digestion and purity were confirmed by size exclusion chromatography. For Fab labeling, Alexa Fluor 488 and Alexa Fluor 647 antibody labeling kits (ThermoFisher) were used as per the manufacturer's protocol. For cell labeling, 1 ml of 5 x 10 5 cells/ml was incubated with Fab (1-10 nM) on ice for 25 minutes. Cells were washed three times in PBS (phosphate buffered saline, pH 7.4).

Fluorescence-activated cell sorting and quantification of protein expression
Wild type or transduced Jurkat and HEK293T cells were washed once in ice-cold PBS, and 1 million cells were incubated with appropriate antibodies (isotype control, eBioscience, UK; Gap 8.

HaloTag® labeling
Cells expressing HaloTag® (Promega, UK) fusion protein (Lck, TCR) were labeled with TMR Cell* following the manufacturer's preparation protocol (www.promega.co.uk/products/imaging-andimmunological-detection/cellular-imagingwithhalotag/proteintrafficking). First, the cell medium was replaced with 200 µl RPMI without supplements to which 1-5 µM of Halo-Tag TMR dye was added, and the cells then incubated at 37°C for 45 minutes. To ensure that free dye would not remain in the cytoplasm, cells were washed three times in HBS and then further incubated at 37°C for 30 minutes followed by another three washes with PBS.

Sample preparation for calcium response measurements
Jurkat T-cells were labeled with 4 µM Fluo-4 AM (F-14201; Invitrogen, UK) for 30 min at room temperature with 2.5 mM probenecid (P-36400; Invitrogen, UK) in RPMI (Sigma-Aldrich, UK) without supplements. Cells were then washed in HBS (51558; Sigma, UK) and the medium changed to HBS containing 2.5 mM probenecid before their addition to the microscope sample container with the prepared microscope coverslip.

Total internal reflection microscopy (TIRFM)
For all Figures containing TIRFM data (except Fig. S4  were directed into the objective lens, resulting in a power density at the sample of ~1 kW/cm 2 and 100 W/cm 2 respectively. The fluorescence signal was separated from the laser excitation by a quadband dichroic filter (Di01-R405/488/561/635-25x36, Semrock). Additional isolation of the fluorescence signal was achieved by long-pass and band-pass filters placed directly before the detector.

Supported lipid-bilayer (SLB) preparation
Prior to SLB formation on glass cover slips, the cover slips (size no. 1: 0.13 mm in thickness, VWR International, UK) were cleaned by incubation in Piranha solution (

Sample preparation for imaging (TIRFM)
Before imaging, approximately 10 6 cells were resuspended in PBS and incubated in a microcentrifuge tube with the desired antibody fragments for 30 min at room temperature (22°C). After the incubation step, the cells were washed three times with PBS by centrifugation and resuspension of the pellet (600×g, 2 min). After the slides were transferred to the microscope stage, the cells were added; imaging was carried out within the first minutes following cell attachment at room temperature.

Sample preparation for imaging (DHPSF)
Jurkat CD48 + T-cells were labelled with Alexa 647 anti-CD45 antibody (Gap8.3) as previously described before being fixed in 4% paraformaldehyde (Sigma-Aldrich) and 0.2% glutaraldehyde  (Tokunaga, et al., 2008). After reconstruction, a rolling-mean of the fiducial marker's position over 50 frames was used to correct for drift in x, y and z.

Image analysis (TIRFM experiments)
Image analysis was performed using a combination of manual analysis (ImageJ, U. S. National Institutes of Health, Bethesda, Maryland, USA, http://imagej.nih.gov/ij/) and custom-written MATLAB code (MATLAB R 2014b, The MathWorks, US).

i) Image acquisition and analysis for single-molecule tracking experiments at close contacts on SLBs
Videos were obtained at a frame rate of 28.6 frames per second ( custom written MATLAB routine. Using these binary images, the MATLAB routine also sorted the trajectories into two categories ("confined within" and "outside" the contact). The diffusion coefficients for these two categories of trajectories were extracted as described elsewhere (Weimann et al. 2013). The number of classified trajectories for a given cell was normalized against the corresponding mask area, i.e. the area "inside" and "outside" the contact, respectively.

ii) Image acquisition and analysis for simultaneous imaging of CD45 distribution in the close-contacts on SLBs and Ca 2+ signaling (Fluo-4 fluorescence increases) with TIRFM
Data (videos) were acquired on the TIRF microscope as described above at 37°C, using the 488 and 633 lasers for excitation and the corresponding dicroics and emission filters. Data were acquired using alternating excitation and time-lapse acquisition, with an exposure time of 100 ms, and a time between frames of 2 s. The videos were analyzed using custom-written MATLAB code. Briefly, cell positions were manually traced in the last frame of the Fluo-4 channel, and for each cell its mean intensity trace across the entire image sequence was calculated. The time of landing (tland) and Ca 2+ release (tCa) were determined in a semi-automated fashion from these intensity traces; tland was determined manually from the bright field image and tCa automatically by finding peaks in the derivative of the intensity trace. The time taken to trigger was defined as tCa-tland. For the interval tland to tCa, the area of cell-surface contact was calculated from the CD45 channel for each cell by manually tracing the area inside the close contact outlined by CD45 fluorescence in a programintegrated GUI. From this analysis, we obtained the change of cell-surface contact area for individual cells until the time point of Ca 2+ release, tCa. All further statistical analysis and fits of the traces were performed with Origin (OriginPro 9.1 G, OriginLab Corporation, Northampton, USA).

iii) Super-resolution microscopy of CD45 distribution in Jurkat T-cells
CD45 was labeled with Gap8.3 conjugated to the fluorescent dye Atto655 and made to emit intermittently by the addition of ascorbic acid (100 µM; for details see Vogelsang et al., 2009).
Videos of isolated fluorescent puncta could thus be obtained whose center positions were extracted using the software PeakFit (www.sussex.ac.uk/gdsc/intranet/microscopy/imagej/smlm_plugins), an ImageJ plug-in for super-resolution analysis. Briefly, local maxima in each frame were fitted with a 2D-Gaussian described by seven parameters (position on two axes, standard deviation on two perpendicular axes and angle to the horizontal axis, amplitude, and offset). Finally, each singlemolecule position was re-plotted using a custom macro written in ImageJ (http://rsb.info.nih.gov/ij/) as a 2D Gaussian profile defined by the measured integrated intensity and a width given by the average statistical error in localization of the center (95% confidence interval, averaged over all single-molecule localizations); for further details see Ptacin et al., 2010.

iv) DHPSF experiments
All DHPSF data was analysed by easy-DHPSF software (Lew et al., 2015) and rendered using ViSP  Tables   Table S1 Quantitative analysis of close contacts formed by T cells interacting with rCD2-presenting SLBs, and organization of key signaling proteins within these regions measured using single-molecule fluorescence microscopy.

III. Supplementary
Values were obtained from the types of experiments shown in Fig. 2. The automated procedure used to analyze the images and characterize the cell/SLB contacts is described in the Online Methods. 1 Trajectories were classified as "confined" if they could be mapped exclusively onto the inner area of a contact (denoted by "1" in the binary representation of the contacts, c.f. Fig. 2B-D, right panels). 2 Ratio of a molecule's density inside the contact over its overall density in the visible region of the cell. Cell surface area (µm 2 ) 415 5

# Cells/ contacts
Number

V. Supplementary Movies
Movie S1 Animation showing changes in TCR occupation-probability density across a growing close contact over time. The probability of occupation is plotted on the z-axis, the 'time' given in the title is the time post initial contact, and the 'remaining mass' refers to the probability that the TCR is still found within the close contact. Close-contact growth rate is set to g = 0.1 µm 2 /s.
Representative video showing simultaneous rCD2 accumulation and CD45RABC-Halo segregation from stable cell/SLB contacts for CD48 + Jurkat T-cells interacting with a rCD2and CD45RABC-Halo presenting SLB (rCD2:CD45RABC-Halo ratio of 4:1). The video combines raw data for the CD2 channel (i.e. Alexa Fluor 488-tagged CD2 fluorescence, green; left) with a simultaneously-acquired video of the CD45RABC-Halo channel (TMR labelled CD45RABC, red; right). The video plays 10-fold faster than real-time (5 frames per second).

Movie S3
Imaging