T-cell Receptor Is a Threshold Detector: Sub- and Supra-Threshold Stochastic Resonance in TCR-MHC Clusters on the Cell Surface
<p><span class="html-italic">TCR structure mirrors noncognate–cognate dichotomy.</span> Structural proof that TCR is a threshold detector. <span class="underline">Panel <b>A</b></span><span class="underline">:</span> In the first phase of TCR triggering, TCRs scan the surface of the APC without coreceptors. <span class="underline">Panel <b>B</b>:</span> Although in the first phase mainly low-affinity pMHCII bind, sometimes, dictated by the relative abundance, high-affinity or cognate pMHCII (cognate ligand), shaded square, can also bind. <span class="underline">Panel <b>C</b>:</span> During the second phase of TCR triggering, TCR scanning happens in the delimited spatial region called the immune synapse (IS), in the presence of a coreceptor (CD4, in blue) in close proximity to TCR. <span class="underline">Panel <b>D</b>:</span> In the second phase of TCR triggering, the signaling is mainly due to the binding of high-affinity, cognate pMHCII.</p> "> Figure 2
<p><span class="html-italic">Sub- and supra-threshold SR in TCR triggering.</span> Stochastic pooling network (SPN) model of the TCR array [<a href="#B28-entropy-24-00389" class="html-bibr">28</a>,<a href="#B29-entropy-24-00389" class="html-bibr">29</a>,<a href="#B30-entropy-24-00389" class="html-bibr">30</a>,<a href="#B31-entropy-24-00389" class="html-bibr">31</a>,<a href="#B71-entropy-24-00389" class="html-bibr">71</a>]. <span class="underline">Panel <b>A</b>:</span> Surface scanning by a single TCR. While in the first phase of triggering TCR detects both the noncognate and cognate peptides, in the second phase it detects mainly cognate ones by way of high tuning the threshold with coreceptor (not indicated) proximity. Threshold level has been adjusted based on the first phase detection. Because the threshold level has been adjusted to the net effects of both low- and high-affinity pMHCs, in the second phase, a portion of cognatepMHCs becomes subthreshold. For these pMHCs the subthreshold SR effect might be advantageously exploited to be detected. It is also visualized that for a single detector, the temporal behavior of output signal, red-white-green series of bars, might substantially differ from that of the input signal. Symbols: gray circle, noncognate peptide; red square, cognate peptide. <span class="underline">Panel <b>B</b>:</span> Schematic of single TCR scanning. In each moment, at the output a 0 (zero) or 1 (one) is assigned to the input, implying a 1-bit information transfer. Note that signal’s nature has been transformed from a continuous input to a digital output by SR. <span class="underline">Panel <b>C</b>:</span> Surface scanning by a TCR array. In the second phase of TCR triggering, although both the noncognate and cognate peptides are interrogated, only the cognate ones enable activating signals. <span class="underline">Panel <b>D</b>:</span> The equivalent pooling network model of the TCR array. Note that the signal’s nature has been transformed from a continuous input to a digital output by SSR.</p> "> Figure 3
<p><span class="html-italic">Types of gating with threshold distributions. Mean-threshold gating with centered signal and threshold distributions.</span> Due to noise, the originally single-valued threshold (θ, marked by dashed vertical in black) becomes distributed (Gaussians marked by red colour), in the intervals delimited by the green vertical bars. The portions of signal distributions (Gaussians marked by black colour) affected by the threshold distributions are marked by orange shading. The net degree of influence is represented by the overlap regions of the threshold and signal distributions. Information transmission by the TCR array [<a href="#B31-entropy-24-00389" class="html-bibr">31</a>]. By opening out the threshold distribution, the intensity of sampling from the left, originally sub-threshold portion of the signal distribution is gradually increased at the cost of decreasing sampling from the right, originally supra-threshold portion. <span class="underline">Panel <b>A</b>:</span> Nominal threshold level of individual detectors in the TCR array of <a href="#entropy-24-00389-f002" class="html-fig">Figure 2</a> is designated by θ. Its position is marked by a vertical green thick line on the horizontal axis of the detected signal, whose distribution is represented as a Gaussian black curve with standard deviation (width parameter) σ. The detected signal can be the affinity of pMHC binding itself or any signal proportional to it, e.g., extent of conformational change in TCR, size or duration of force arisen between TCR and pMHC. <span class="underline">Panel <b>B</b>:</span> The action of independent identically distributed random noises on the inputs of the TCR array can be conceived as the nominal threshold θ would be distributed on θ<sub>1</sub>, θ<sub>2</sub>, …, θ<sub>N</sub> according to some noise distribution, symbolized by the red curve, with standard deviation σ<sub>1</sub>. The working function of the TCR array now can be summarized as to take random samples from the signal distribution with the aid of the threshold distribution. The quality of sampling and ultimately that of the information transmission from the signal distribution is dictated by the degree of overlap between the signal and threshold distributions. In Panel <b>B</b>, sampling is performed mainly from the middle of signal distribution corresponding to undersampling, the standard deviation of threshold (σ<sub>1</sub>) being much smaller than that of signal, σ<sub>1</sub> < σ. <span class="underline">Panel <b>C</b>:</span> The sampling by noise is optimal, and the transmitted information is the maximal, when the standard deviation of noise (σ<sub>2</sub>) equals that of signal σ<sub>2</sub> = σ. Here, the whole range of signal distribution is sampled, at the cost of reduced sampling from the right portion of the signal distribution. <span class="underline">Panel <b>D</b>:</span> Information transmission is also not optimal when the noise distribution is wider than that of signal, σ<sub>3</sub> > σ. Here only a portion of the information transmitting capability or “channel capacity” of the TCR array as an information channel is utilized. Equivalently, due to the unnecessarily large width of threshold distribution, sampling density from the range of signal is reduced. From Panels <b>A</b>–<b>D</b> also the most important attribute of SSR can be read off, namely, the existence of special noise level, where the transmitted information is maximal, for a given array size.</p> "> Figure 4
<p>Types of gating with threshold distributions. Off-centered signal and threshold distributions, case I: signal mean smaller than threshold mean (sub-threshold gating). The effect of increasing noise level when the signal is entirely sub-threshold [<a href="#B31-entropy-24-00389" class="html-bibr">31</a>]. Information transmission is gradually improved by opening out the threshold distribution. At the end, although the whole signal range is sampled, the sampling density is reduced due to the shallowing of the threshold distribution. By judging from the shape of the overlap region, the symmetric signal distribution will be skewed to the left after the asymmetric sampling. <span class="underline">Panel <b>A</b>:</span> Nominal threshold level of individual detectors in the TCR array of <a href="#entropy-24-00389-f002" class="html-fig">Figure 2</a> is designated by θ. Its position is marked by a vertical green thick line on the horizontal axis of the detected signal, whose distribution is represented as a Gaussian black curve with standard deviation σ. The signal now is entirely subthreshold, because the whole distribution is located left to θ. <span class="underline">Panel <b>B</b>:</span> Upon the action of independent random noises at each input of the TCR array, the nominal threshold θ becomes distributed on θ<sub>1</sub>, θ<sub>2</sub>, … θ<sub>N</sub> according to the noise distribution, symbolized by the red curve, with standard deviation σ<sub>1</sub>. Sampling is performed by the threshold distribution mainly from the right tail of signal distribution, marked by orange shading, corresponding to heavy undersampling, the standard deviation of threshold (σ<sub>1</sub>) being much smaller than that of signal, σ<sub>3</sub> << σ. <span class="underline">Panel <b>C</b>:</span> By equalizing the widths of noise and signal distributions, σ<sub>2</sub> = σ, sampling becomes better as judged from the larger orange overlap area (half the signal), but yet remaining undersampling. <span class="underline">Panel <b>D</b>:</span> Information transmission is the best, when the noise distribution becomes wider c.a. double of that of signal, σ<sub>3</sub> = 2σ. Upon a further increase in the width of noise distribution, new empty thresholds left to the signal range tend to appear.</p> "> Figure 5
<p>Types of gating with threshold distributions. Off-centered signal and threshold distributions, case II: signal mean larger than threshold mean (suprathreshold gating). The effect of increasing noise level when the signal is entirely suprathreshold [<a href="#B31-entropy-24-00389" class="html-bibr">31</a>]. Here only detrimental effects of noise on information transmission can be revealed. By gradually increasing the width of threshold distribution an increasing portion of the originally suprathreshold signal distribution becomes sub-threshold, resulting in a gradual undersampling of the left side of the signal distribution. <span class="underline">Panel <b>A</b>:</span> Nominal threshold level of individual detectors in the TCR array of <a href="#entropy-24-00389-f002" class="html-fig">Figure 2</a> is designated by θ. Its position is marked by a vertical green thick line on the horizontal axis of the detected signal, whose distribution is represented as a Gaussian black curve with standard deviation σ. The signal now is entirely suprathreshold, meaning maximal information transfer, because the whole distribution is right to θ. <span class="underline">Panel <b>B</b>:</span> Upon the action of independent random noises at each input of the TCR array, the nominal threshold θ becomes distributed on θ<sub>1</sub>, θ<sub>2</sub>, … θ<sub>N</sub> according to the noise distribution, symbolized by the red curve, with standard deviation σ<sub>1</sub>. Sampling is preferentially performed now by the threshold distribution from the right tail of signal distribution, the complement of the orange shaded area, corresponding to undersampling, the standard deviation of threshold (σ<sub>1</sub>) being much smaller than that of signal, σ<sub>1</sub> << σ. <span class="underline">Panel <b>C</b>:</span> By equalizing the widths of noise and signal distributions, σ<sub>2</sub> = σ, sampling becomes worse, meaning heavier under-sampling, as judged from the larger orange overlap area (half the signal range). <span class="underline">Panel <b>D</b>:</span> Information transmission is the worst, when the width of the noise distribution becomes equal with the double of that of signal, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>2</mn> <mo>·</mo> <mi>σ</mi> </mrow> </semantics></math>.</p> ">
Abstract
:1. Introduction
2. Properties of the TCR-MHC System Analyzed from the Viewpoint of SR
2.1. TCR Behaves as a Threshold Detector
2.1.1. Structure and Signaling of TCR
2.1.2. The Noncognate–Cognate Dichotomy Is Mirrored by the TCR Structure
2.1.3. TCR Triggering as a Biphasic Process: Adaptive Thresholding
2.2. SSR in TCR Clusters
2.2.1. TCR Array as an “Equivalent Pooling Network”
2.2.2. Signal Transmission by SSR
2.2.3. Noise’s Nature
2.3. Qualifying CARs with SR
3. Discussion
3.1. Two Levels of SR in Immune Recognition
3.2. SR in TCR and MHC Arrays: SSR
3.3. Exploiting SSR to Optimize Molecular Prostheses
3.4. Förster (Fluorescence) Resonance Energy Transfer (FRET) as an Information Channel
3.5. SSR as an Analogue-to-Digital Signal Converter (ADC)
3.6. Future Directions and Limitations of the SR Model
3.7. Metastases Finding as a Problem of Weak “Fault Signal” Detection
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
AFM | atomic force microscopy, |
APC | antigen presenting cell, e.g., dendritic cell, |
CAR | genetically engineered chimeric antigen receptor, composed of the variable and constant regions of the antigen recognising Fab portion of antibody connected by a linker region, as well as a spacer and transmembrane region, and an intracytoplasmic domain containing 3–5 (signaling) sites, which can be phosphorylated, depending on the generation of CAR (1th–4th), |
CD28 | coreceptor (signal amplifier) on the side of TcR on a T cell in apposition to an APC, its counter receptor is CD80, |
CD45/CD148/CD137 | phophatases, dephosphorilate sites, which can be phophorylated, act against kinases, |
CD8/CD4 | coreceptors (signal amplifiers) CD8 and CD4 on T cells—killer and helper, respectively–, binding to MHCI and MHCII, respectively on an APC in apposition to a T cell, |
cSMAC/pSMAC/dSMAC | central, peripheral, and distal supramolecular activation clusters, concentric zones—centripetally from inside to outside—constituting the immune synapse (IS) on T cells, rich in non-signaling TcRs |
(cSMAC) | microclusters of signaling TcR and LFA-1 (pSMAC), and rich in CD45 (dSMAC), |
FRET | Förster (or fluorescence) resonance energy transfer, occuring between an energy donor and an energy acceptor when their distance is between 1 nm and 10 nm, |
ICAM-1/ICAM-2 | intracellular adhesion molecules type 1 and type 2, on the surface of an APC, binding to LFA-1/LFA-3 on the recognising T cell, |
IS | immune synapse, consisting of concentric zones called cSMAC, pSMAC, and dSMAC, |
ITAM | tyrosine based activation motif, which can be phosphorylated, or docking site for tyrosine kinases Lck, Src, |
Lck | Src tyrosine kinase p65lck, |
LFA-1/LFA-3 | leukocyte function associated antigen type 1 and type 3 on the side of TCR on the recognising T cell, its counter receptor on the APC is ICAM-1/ICAM-2, capable also for signaling, |
MHCI/MHCII | Major Hystocompatibility Gene Complex products I and II, presenting antigen of the surface of an APC towards effector cells, killer and helper T cells, respectively, |
pMHC | MHC molecule presenting short—8–9 amino acids long—peptide fragment of antigen on the surface of APC towards the recognising receptor TCR on the surface of an effector (killer, helper, memory) T-cell, |
SR | stochastic resonance, |
SSR | supra-threshold stochastic resonance, |
TcR | T-cell receptor—composed of a heterodimer of TCRα and TCRβ (briefly αβ) recognising the antigen, a long signaling domain TCRζζ (briefly ζζ) containing 6 phosphorilatable sites (ITAMs) and CD3γε (briefly γε), CD3δε (briefly δε) signaling domains each containing 2 sites, which can be phosphorilated—binding to peptide-loaded MHCs on the surface of an APC, |
TEM | transmission electron microscopy, |
TM4SF | transmembrane-4 family protein, accessorical, adaptor protein spanning the membrane four times. |
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Bene, L.; Bagdány, M.; Damjanovich, L. T-cell Receptor Is a Threshold Detector: Sub- and Supra-Threshold Stochastic Resonance in TCR-MHC Clusters on the Cell Surface. Entropy 2022, 24, 389. https://doi.org/10.3390/e24030389
Bene L, Bagdány M, Damjanovich L. T-cell Receptor Is a Threshold Detector: Sub- and Supra-Threshold Stochastic Resonance in TCR-MHC Clusters on the Cell Surface. Entropy. 2022; 24(3):389. https://doi.org/10.3390/e24030389
Chicago/Turabian StyleBene, László, Miklós Bagdány, and László Damjanovich. 2022. "T-cell Receptor Is a Threshold Detector: Sub- and Supra-Threshold Stochastic Resonance in TCR-MHC Clusters on the Cell Surface" Entropy 24, no. 3: 389. https://doi.org/10.3390/e24030389