Natural Killer Cell Receptor Signaling and Activation Depend on Cell Cycle Stages

Natural Killer Cell Receptor Signaling and Activation Depend on Cell Cycle Stages | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Natural Killer Cell Receptor Signaling and Activation Depend on Cell Cycle Stages View ORCID Profile Darren Wethington , View ORCID Profile Indrani Nayak , Helle Jensen , William C. Stewart , Oscar A. Aguilar , Shih-Yu Chen , View ORCID Profile Garry P. Nolan , Gregory K. Behbehani , View ORCID Profile Lewis L. Lanier , View ORCID Profile Jayajit Das doi: https://doi.org/10.1101/2025.02.24.639882 Darren Wethington 1 Steve and Cindy Rasmussen Institute for Genomic Medicine, Abigail Wexner Research Institute at Nationwide Children’s Hospital , Columbus, OH, USA 2 Biomedical Sciences Graduate Program, The Ohio State University , Columbus, OH, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Darren Wethington Indrani Nayak 1 Steve and Cindy Rasmussen Institute for Genomic Medicine, Abigail Wexner Research Institute at Nationwide Children’s Hospital , Columbus, OH, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Indrani Nayak Helle Jensen 3 Department of Microbiology and Immunology and the Parker Institute for Cancer Immunotherapy, University of California-San Francisco , San Francisco, CA, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site William C. Stewart 4 GIG Statistical Consulting, LLC , Columbus, OH, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Oscar A. Aguilar 3 Department of Microbiology and Immunology and the Parker Institute for Cancer Immunotherapy, University of California-San Francisco , San Francisco, CA, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Shih-Yu Chen 5 Institute of Biomedical Sciences, Academia Sinica , Taipei, Taiwan Find this author on Google Scholar Find this author on PubMed Search for this author on this site Garry P. Nolan 6 Department of Pathology, Stanford University School of Medicine , California, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Garry P. Nolan Gregory K. Behbehani 7 Division of Hematology, The Ohio State University , Columbus, OH, USA 8 Pelotonia Institute for Immuno-Oncology, The James Comprehensive Cancer Center, The Ohio State University , Columbus, OH, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Lewis L. Lanier 3 Department of Microbiology and Immunology and the Parker Institute for Cancer Immunotherapy, University of California-San Francisco , San Francisco, CA, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Lewis L. Lanier For correspondence: Jayajit.Das{at}nationwidechildrens.org lewis.lanier{at}ucsf.edu Jayajit Das 1 Steve and Cindy Rasmussen Institute for Genomic Medicine, Abigail Wexner Research Institute at Nationwide Children’s Hospital , Columbus, OH, USA 2 Biomedical Sciences Graduate Program, The Ohio State University , Columbus, OH, USA 8 Pelotonia Institute for Immuno-Oncology, The James Comprehensive Cancer Center, The Ohio State University , Columbus, OH, USA 9 Department of Pediatrics, The Arthur G. James Cancer Hospital and Richard J. Solove Research Institute, College of Medicine , Columbus, OH, USA 10 Biophysics Program, The Ohio State University , Columbus, OH, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Jayajit Das For correspondence: Jayajit.Das{at}nationwidechildrens.org lewis.lanier{at}ucsf.edu Abstract Full Text Info/History Metrics Supplementary material Preview PDF Abstract Receptor signaling in Natural Killer (NK) cells leads to post-translational modification (e.g., phosphorylation) of sub-cellular signaling proteins within minutes of receptor stimulation that eventually give rise to diverse effector functions including cell proliferation. Recent single-cell mass cytometry (i.e., CyTOF) experiments in macrophages showed variations of abundances of phosphorylated signaling proteins across cell cycle states indicating a dependence of cell signaling kinetics on an order of magnitude slower kinetics (~ several hours) of cell cycle transitions. We investigated cell cycle dependence of NKG2D signaling kinetics in NK cells by CyTOF measurements performed on IL-2-treated NKG2D-stimulated primary human CD56 dim NK cells. The CyTOF experiments revealed monotonic or semi-monotonic increases of the average protein abundances of the majority of signaling proteins such as pCrkL, pPLCγ2, and pErk, and the degranulation marker protein CD107a with progressing cell cycle states at specific time points post-NKG2D stimulation; however, several proteins such as pVav1, pS6, and pAkt, and early activation marker protein CD69 also showed non-monotonic variations in the average abundances with progressing cell cycle states. We used minimal mathematical and computational models coupling signaling and cell cycle processes to show that non-monotonic variations in the signaling protein abundances with progressing cell cycle stages are likely to arise in situations where protein synthesis and degradation and signaling kinetics are actively regulated by cell cycle processes. Introduction Natural Killer (NK) cells are lymphocytes of our innate immune system and provide important protection against infection and tumors 1 - 3 . NK cells express a wide array of plasma membrane-bound activating and inhibitory NK cell receptors (NKRs), co-receptors, and adhesion receptors that interact with cognate ligands expressed on target cells 2 . In addition, NK cells express cytokine receptors such as IL-2 receptors that bind to soluble cytokine molecules present in the microenvironment 3 . Subcellular biochemical signaling reactions occurring in the time scales of seconds to minutes 4 - 6 , which are initiated by binding of diverse NKRs, co-receptors, and adhesion, and cytokine receptors under appropriate conditions may lead to NK cell activation 1 , 2 . Activated NK cells unleash a variety of effector functions ranging from cell proliferation, lysis of target cells, or secretion of cytokines such as interferon γ. NK cell division can take orders of magnitude longer time scales (~hours) 7 , 8 to fully manifest compared to the signaling biochemical reactions. A proliferating eukaryotic cell spends most of the time during cell division in the cell cycle interphase where DNA, proteins, and metabolites are synthesized in the cell in preparation for the cell duplication 9 . The interphase is further subdivided into G1, S, and G2 stages that progress through the cell cycle as G1 → S → G2. At the end of the G2 stage, the cell goes through mitosis, M-stage, where the cell division takes place, and the resulting pair of daughter cells can exit the cell cycle by going into a quiescent stage G0 or continue dividing by entering the G1 stage 9 . NKG2D is an activating receptor that transmits signals by its association with the DAP10 adapter protein through charge interactions between the transmembrane segments of NKG2D and DAP10 10 . The cytoplasmic domain of DAP10 possesses a Src homology-2 domain that upon tyrosine phosphorylation recruits and activates the p85 subunit of PI3 kinase and a Grb2-Vav1 complex that triggers NK cell activation and cell-mediated cytotoxicity 10 , 11 . The human NKG2D receptor binds a family of stress-induced ligands (MICA, MICB, and ULBP1-6) that are frequently displayed on the surface of tumor or pathogen-infected cells and render these cells susceptible to NK cell-mediated killing 12 , 13 . NK cells constitutively express an intermediate-affinity IL-2 receptor composed of IL-2Rγ and IL-2Rβ subunits that upon binding to IL-2 or IL-15 transmit activation and growth signals through the JAK – STAT pathway that initiates cellular proliferation 14 . Therapeutics targeting NKG2D and IL-2 are currently under clinical investigation in cancer patients. NK cells undergoing proliferation can reside in different cell cycle stages as they interact with target cells with plasma membrane-bound receptors. As single cells progress through cell cycle transitions many signaling proteins such as kinases and phosphatases, as well as their substrate proteins, are synthesized to maintain a steady per cell copy number or abundance of these proteins during cell growth 15 , 16 . Thus, as single NK cells progress through cell cycle stages the abundances of reacting signaling proteins could change resulting in different abundances of signaling products. For example, the abundance of a phosphorylated form of a signaling protein (e.g., pVav1) could be different in NK cells residing in different cell cycle stages as the abundances of phosphorylating or dephosphorylating enzymes, along with the abundance of the substrate protein (e.g., Vav1) vary across cell cycle stages. In addition, proteins regulating cell cycle processes, such as cyclin dependent kinases (CDKs), can actively participate in chemically modifying signaling proteins 17 , 18 . For example, in HeLa cells the phosphorylation of the site S473 in signaling protein Akt is regulated by CDK2 19 . This produces variations in the abundances of the phosphorylated protein Akt-pS473 similar to that of CDK2 abundances across cell cycle states while the total Akt abundance remains unchanged 19 . In another example, CDK proteins in G2-M state phosphorylate Wnt-binding co-receptor LRP6 promoting Wnt signaling in the state 18 . Single-cell mass cytometry (CyTOF) experiments can simultaneously measure expressions of proteins that can track cell cycle progression and receptor signaling kinetics 20 - 23 . CyTOF experiments performed on human monocyte cell line THP-1 stimulated by TNFα showed that average abundances of modified forms of signaling proteins can depend on cell cycle stages 24 . Here we investigated cell cycle dependence on NK cell signaling and activation by performing CyTOF measurements on IL-2-treated primary human CD56 dim NK cells stimulated by plate-bound anti-NKG2D antibodies at different time points. A total of 40 different proteins were evaluated by CyTOF, mostly pertaining to signaling proteins, activation markers, and cell cycle markers. While the average abundance of the majority of the signaling proteins evaluated showed monotonic or semi-monotonic increases with the progression of cell cycle stages, the average abundances of some proteins such as pAkt, pMAPKAPK2, pPLK1, pS6, pNFκB, and pVav1 also showed non-monotonic variations at specific time points post-NKG2D stimulation. The potential mechanisms that underlie these variations of abundances of signaling products across cell cycle stages can range from changes in the abundances of reacting signaling proteins in different cell cycle stages to active participation of CDK proteins in cell signaling. We developed minimal mathematical and computational models that couple cell cycle transitions and signaling reactions to quantify influences of cell cycle transitions in producing variations in the abundances of signaling proteins across cell cycle states. We find that monotonic increases in the average abundances of phosphorylated proteins with progressing cell cycle states can be produced by protein synthesis/degradation and phosphorylation/dephosphorylation rates that do not change with cell cycle stages. However, the occurrence of non-monotonic changes or decreases in the average abundances of phosphorylated proteins with progressing cell cycle stages calls for specific conditions such as limitation of enzyme concentrations, or direct intervention of cell cycle regulating proteins in phosphorylation/dephosphorylation reactions. Thus, the nature of variation of the abundances of signaling proteins with cell cycle stages can point to different mechanisms of regulation of receptor signaling kinetics by cell cycle processes. Results Phosphoprotein abundances show monotonic and non-monotonic changes with progressing cell cycle stages in NKG2D-stimulated, IL-2-treated primary NK cells The abundances of proteins associated with NKG2D signaling can potentially vary across cell cycle states in NK cells stimulated with NKG2D ligands due to the differences in the abundances of reacting proteins in cells residing in different cell cycle stages or the regulation of the signaling kinetics by proteins (e.g., CDKs) involved in driving cell cycle progression ( Figure 1 ). We investigated the variation of NKG2D signaling proteins in primary human NK cells. Primary human CD56 dim NK cells were treated with IL-2 for 24 hours to prime the NKG2D signaling pathway and then stimulated with plate-bound anti-NKG2D agonist antibodies. NKG2D transmits signals through the DAP10 adaptor protein, which recruits and activates the phosphatidylinositol 3-kinase 10 . The NK cells were profiled at 2, 4, 8, 16, 32, 64, and 256 minutes post-NKG2D stimulation using CyTOF 25 , which assayed 31 different signaling proteins and surface markers simultaneously ( Figure 2A ). The various cell cycle stages (i.e., G0, G1, S, and G2 + M) were gated using UMAP based on the cell cycle markers, 5-iodo-2-deoxyuridine (IdU), cyclin B1, phosphorylated histone 3 (pH3), phosphorylated retinoblastoma protein (pRb) and Kiel 67 (Ki67) ( Figure 2B , Supplementary Figure S1 ). Further details regarding the analysis are provided in Materials and Methods. ~10-20% of the NK cells were in G0, ~60-70% were in G1, and ~10% were in S and G2 + M stages, respectively, throughout the various time points post-NKG2D stimulation (see Figure 2C and Figure 2D ). The variations of the average protein abundances across cell cycle stages G1, S, and G2 + M post-NKG2D stimulation were analyzed as follows. We classified the variations into nine different types (see labels in Figure 2E ) based on the change, namely, rise, or decay, or no-change, in the average abundance between G1 to S, and S to G2+M for each time point by performing one-sided t -tests. Because the protein distributions follow non-normal distributions, we natural log-transformed the protein intensities before performing the t -test comparing average abundances of proteins residing in different cell cycle states ( Figure 2E ). More details are provided in Methods. At t = 0 min (i.e., unstimulated state of the IL-2-treated CD56 dim NK cells), 8 proteins that were not related to cell cycle displayed significant increases from G1 to S and S to G2-M, and the majority of the proteins (22 out of 31 showed no change between G1 to S followed by a rise from S to G2 + M stage ( Figure 2E ). Next, we investigated the variation of the average abundances with cell cycle stages at multiple time points post-NKG2D stimulation. The majority (~ 89%) of the proteins showed a strictly monotonic increase (i.e., increase for G1 → S and increase for S → G2 + M) or a semi-monotonic increase (i.e., non-change for G1 → S and increase for S → G2, or vice versa) with progressing cell cycle stages between 2 to 256 mins signaling kinetics. Proteins involved in cell signaling that showed monotonic or semi-monotonic behavior post-NKG2D stimulation included pCrkL, pPLCγ2, pAkt, pMAPKAPK2, pSLP76, pNFκB, pErk1-2, pPLK1, p38, pLAT, pZAP70, pS6, and pVav1. Interestingly, 12 proteins (~ 9%) including pAKT, pMAPKAPK2, pNFκB, pPLK1, pS6, and pVav1 also showed non-monotonic behavior in protein abundances at specific time points post-NKG2D stimulation marked by a decrease for G1→ S followed by an increase from S to G2 + M ( Figure 2E ). We did not find any protein showing a monotonic decrease, i.e., decrease for G1→ S and decrease for S → G2 + M. The early cell activation marker, CD69, showed non-monotonic behavior at 32, 64, and 256 min post-NKG2D stimulation ( Figure 2E-2G ). CD107a is a marker of NK cell activity, indicating degranulation and cytotoxic function when present on the cell surface. The average CD107a protein abundances exhibited monotonic or semi-monotonic behavior at all time points with the highest levels observed at 256 min post-NKG2D stimulation. These highest abundances displayed semi-monotonic behavior with progressing cell cycle states ( Figures 2E and 2G , Supplementary Figure S2 ). In summary, in NKG2D receptor-stimulated primary NK cells the average abundances of most of the measured signaling proteins, as well as the two activation markers, followed a strictly monotonic or semi-monotonic increase with progressing cell cycle states for most time points, with certain proteins such as pAkt, pMAPKAPK2, pNFκB, pPLK1, pS6, and pVav1 showing non-monotonic changes at specific time points post-NKG2D stimulation ( Supplementary Figure S2 ). Download figure Open in new tab Figure 1: Potential influences of cell cycle transitions on NKG2D receptor signaling kinetics in NK cells. Schematic depiction of potential mechanisms with which cell cycle transitions can regulate NKG2D receptor signaling. As an NK cell progresses through cell cycle stages, the abundances of many proteins including ones involved in NKG2D signaling can increase. The time scale ( t signaling ) for cell signaling is typically in seconds to minutes and can be 10-100× smaller than the timescales ( t cell cycle ) of cell cycle transitions which can take hours to occur. The cell volume increases with cell cycle progression as well. The combined effect of increasing protein abundances and the cell volume can increase or decrease the frequency at which second-order biochemical signaling reactions occur. This can result in different abundances of signaling products arising from second order signaling reactions in different cell cycle stages. In addition, cell cycle regulating CDK-cyclin complexes can potentially influence post-translational modifications of signaling proteins in specific cell cycle stages affecting NKG2D signaling kinetics. Download figure Open in new tab Figure 2: Variation of the abundances of signaling proteins in NKG2D-stimulated primary human NK cells residing in different cell cycle stages. (A) IL-2 treated primary CD56 dim NK cells were analyzed by CyTOF at 0 (i.e., unstimulated), 2, 4, 8, 16, 32, 64, and 256 min post-NKG2D stimulation. Cell populations were gated using UMAP embeddings into various cell cycle stages for different time points. Protein intensities follow asymmetric log-normal distributions across cell cycle stages. We log-transformed the protein intensity data to compare mean protein abundances in cell populations at different cell cycle stages (e.g., G1 and S or S and G2-M). We used one sided t- test for the comparison. (B) Cell populations are gated into G1, S and G2-M stages for different time points using cell cycle markers (see Methods). (C) Proportion of cells (in percentage) at different cell cycle stages are shown at 0 and 256 min post-NKG2D stimulation. (D) Proportion of live CD56 dim NK cells in G0, G1, S and G2-M stages are shown at the different time points post-NKG2D stimulation. (E) The variations of the mean log e (Intensity) of signaling proteins across cell cycle transitions, G1→ S, and S → G2+M, are shown in terms of nine different types of variations. A change (increase or decrease) is marked when the change in the mean log e (Intensity) from G1→ S, or S→G2+M, has a statistical significance level α = 0.05 in one sided t- test. The nine types are characterized by the changes in (G1→ S, S → G2+M) as follows: (increase, increase), (increase, no-change), (no-change, increase), (increase, decrease), (decrease, increase), (decrease, no-change), (no-change, decrease), (decrease, decrease), (no-change, no-change). (F) Shows histograms of protein intensities for untransformed (raw) data at different time points across cell cycle stages. The colors of the histograms represent the arithmetic mean. (G) The variation of geometric mean of protein intensities per cell are shown at different time points post-NKG2D stimulation (see label) for pPLCγ2, pVav1, CD69 and CD107a. Red dashed lines are used to guide monotonic increase of pPLCγ2 at 16 min and CD107a at 64 min post-NKG2D stimulation, non-monotonic behavior (decrease-increase) of pVav1 and CD69 at 4 min and 256 min post-NKG2D stimulation across cell cycle stages, respectively. To investigate differences in the interplay between NKG2D signaling and cell cycle progression between NK cell lines and primary NK cells, we analyzed NKG2D signaling kinetics in a human NK cell line, NKL, which constitutively expresses the activating human NKG2D receptor. The NKL cells were stimulated by plate-bound anti-NKG2D. A similar analysis of changes in average signaling protein abundances with cell cycle states revealed a larger fraction (~15%) of proteins displaying non-monotonic variations post-NKG2D stimulation ( Supplementary Figure S3 ). Both in NKL and primary NK cells stimulated with anti-NKG2D, the early activation marker CD69 exhibited non-monotonic behavior at a few time points late in the signaling kinetics. For all other earlier time points, CD69 displayed semi-monotonic behavior across cell cycle stages in primary NK cells as opposed to no changes in the abundances across cell cycle stages in NKL cells ( Supplementary Figure S3 ). The abundances of the degranulation marker CD107a increased semi-monotonically in both NKL and primary NK cells for most time points during NKG2D signaling kinetics. However, in NKL cells, CD107a showed a non-monotonic behavior, with the highest expression at 256 minutes. The abundance of the signaling protein pS6 showed non-monotonicity in both NKL and primary NK cells at certain time point and showed monotonic or semi-monotonic behavior at most timepoints in primary NK cells, whereas in NKL cells, there were no changes in the abundances. In addition, we engineered the NKL cells to express activating mouse receptor Ly49H to study another NKR signaling kinetics that uses the ITAM-bearing adaptor and the DAP10 adaptor, in contrast to human NKG2D receptor signaling, which solely uses the DAP10 adaptor 12 , 26 . Anti-Ly49H antibodies were used to stimulate Ly49H-expressing NKL cells, and a similar analysis to the one above showed a higher fraction (~17%) of signaling proteins displaying non-monotonic changes compared to those in NKG2D-stimulated primary human NK cells ( Supplementary Figure S4 ). A marked difference between NKG2D stimulated primary NK cells and NKL cells with Ly49H stimulation was no changes in the abundances of CD69 or CD107a across cell cycle stages for the majority of the time points during the signaling kinetics ( Supplementary Figure S4 ). A few proteins showing non-monotonic changes with cell cycle stages upon Ly49H stimulation, which differed from the behaviors observed in NKG2D-stimulated NKL cells included pSTAT1, DAP12, and CCR7. The monotonic and non-monotonic variations in the average protein abundances with progressing cell cycle states can arise due to various mechanisms as cells progress through cell cycle states such as (a) variations in the average abundances of interacting signaling protein (i.e., substrate, kinase or phosphatase), (b) increase in the cell size (volume), and (c) potential interactions of CDKs with cell signaling proteins. To elucidate mechanisms how these processes influence the abundances of signaling proteins at different cell cycle stages, we developed a set of minimal models that consider basic components of biochemical signaling reactions coupled with cell cycle processes. Furthermore, each of these processes is stochastic in nature, giving rise to randomness in both the duration of cell cycle stages and the production of signaling proteins. Therefore, we considered stochastic time evolution of our model systems. We developed our models in two steps: first, we considered models that can be solved analytically, and exactly and then we developed a stochastic simulation method, validated by the analytical calculations, to simulate the model kinetics. Next, we extended our models to include non-linear biochemical reactions, which were numerically simulated using our stochastic simulation approach. Development of minimal models that couples first-order cell signaling reactions and cell cycle processes We developed a minimal model that combines signaling reactions with processes involved in cell cycle transitions. In this model, an unphosphorylated protein species A (e.g., Vav1, Erk) undergoes post-translational modifications such as tyrosine phosphorylation through a first-order reaction. Such a protein phosphorylation can occur during signaling kinetics initiated by the stimulation of NK cell receptors (e.g., NKG2D) and cytokine receptors (e.g., IL-2R). The phosphorylated form of A (denoted as A*) is dephosphorylated by phosphatases in the cell. The protein species A can be produced or degraded in individual cells residing in different cell cycle states. The synthesis, degradation, phosphorylation, and dephosphorylation of protein species A are modeled by zero- and first-order reactions occurring at rates r, δ, r p , and r d , respectively ( Figure 3A ). We represent the parameter set {r, δ, r p , r d } by a parameter vector θ for brevity. This model is amenable to exact analytical calculations, which helps in clearly deciphering the interplay between cell signaling and cell cycle processes. The description of phosphorylation/dephosphorylation reactions by first-order reactions is reasonable when the abundances of kinases and phosphatases are in excess compared to the substrate abundance 27 . The details of the rates for the reactions are provided in the captions of Figure 3A . Download figure Open in new tab Figure 3: Kinetics of average protein abundances in single cells residing in different cell cycle stages for a first-order signaling reaction model. (A) Schematic representation of a protein phosphorylation-dephosphorylation model involving first-order reactions. Receptor signaling (implicit) leads to phosphorylation of a protein A U (unphosphorylated form) to A* (phosphorylated form). A U is synthesized inside the cell and both A U and A* can be degraded in the cell. The rates of the reactions are shown in the schematic figure. (B) Schematic representation of a cell going through different cell cycle stages: G1, S, G2 and M. Each cell cycle stage consists of multiple intermediate stages, where the cell transitions from stage β to stage β +1 at a rate k β . The protein content of the mother cell in the M stage is divided between two daughter cells upon division following a binomial distribution. In the full heritability scenario, phosphorylated proteins in the mother cells are transferred to the daughter cells. In the non-heritability scenario, only the phosphorylated forms of proteins are de-phosphorylated upon transfer to daughter cells. (C) Shows the population averaged relative cell number or the proportion of average cell number in each cell cycle state. (D) Average protein abundances as a function of time in cell cycle stages for the signaling model shown in ( A) , obtained from Gillespie simulation (circles) or the numerical solution of the ODEs (solid lines). The left panel shows the case when the reaction rates are independent of the cell cycle stages, while the right panel shows the case when the phosphorylation rate of A U is increased 10 times in the S state. We used the following model parameters for the results shown: (left panel) r = r p = r d = 1.0, δ = 0.01, k β = [0.07, 0.1, 0.2, 0.7] in arbitrary units (a.u.), and (right panel) same as in the left panel, except, r p =10.0 in the S state. Next, we combined the above signaling, protein production and degradation processes with cell cycle transitions ( Figure 3B ). We considered that single cells can be in multiple virtual cell cycle states {1, 2,…, β ,…, N }, where the cell cycle transitions between these states occur at the rates described below: These transitions are described as Markovian 28 processes where the transition to the next step depends only on the current state and the residence time of the single cells in each cell cycle state β follows an exponential distribution. The total number N of virtual cell cycle states and the transition rates { k β } can be chosen to fit experimentally measured probability distribution functions of cell division times 17 . The states {β} describe a collection of intermediate virtual states that correspond to a specific cell cycle stage (e.g., S stage). The durations of these intermediate virtual states are exponentially distributed and the durations of cell cycle states consisting of multiple of these virtual states follow an Erlang distribution 29 . This construct effectively models the residence times of cell cycle states observed in experiments 29 . Similar mathematical models have been widely used to describe cell cycle kinetics 30 - 32 . In our model, as a single cell transitions from the current state β to the next cell cycle state β+1, the abundances of unphosphorylated and phosphorylated forms of A in state β, given by ( a U ) β and ( a * ) β , respectively, are fully transitioned to the state β+1. When the mother cell splits into two daughter cells, described by the N → 1 transition, the total number of A molecules in a single cell in the terminal cell cycle state N (i.e., a N = ( a U ) N + ( a * ) N ) is split into the two daughter cells with abundances m and a N -m in cell cycle state β =1, with a binomial probability This assumption has been supported by experiments and has been incorporated into mathematical models describing cell cycle kinetics 33 , 34 . Single cell experiments in yeast cells responding to stress show the heritability of phosphorylated forms of proteins during mitosis 35 ; therefore, we considered this possibility in our model. The transition of the phosphorylated protein abundance ( a * ) N in state N to the daughter cells is considered in two ways ( Figure 3B ): (1) No heritability : The newly generated daughter cells at state 1 do not retain any phosphorylated A* molecule from the mother cell at state N. (2) Full heritability : The number of phosphorylated A* molecules (or a *) in the mother cell at the time of cell division is split into m* and ( a *) N -m* in the daughter cells, with a binomial probability ( Figure 3B ). The time scales pertaining to protein phosphorylation/de-phosphorylation occur on the order of seconds to minutes 4 , 5 , 36 , 37 , whereas mammalian cells usually duplicate in 24 hours 38 . In such cases, the time scales for progression in cell cycle states and signaling kinetics appear to be well-separated. However, the synthesis and degradation of some proteins can occur over longer time scales that can overlap with the above ranges, e.g., protein production can take anywhere from ½ hour to tens of hours 39 and protein degradation via ubiquitylation can occur within ~1 hour to a few hours 40 . Further details regarding these time scales are provided in Table 1 and supplementary Table S1 . Furthermore, the protein synthesis and degradation rates can vary across cell cycles states, and CDK proteins can actively participate in post-translational modifications of signaling proteins – all of which could contribute to variations in the abundances of signaling proteins across cell cycle states. To investigate the roles of these different mechanisms, we considered two scenarios ( neutral and active ) regarding potential cell cycle dependence of synthesis, degradation, phosphorylation, and dephosphorylation rates of signaling proteins in our models. (1) Active case: In this scenario, these rates assume different values ({ θ β }) for different cell cycle states β representing active participation of cell cycle processes in regulating signaling protein production and signaling kinetics. (2) Neutral case: In this case, the rates θ are the constant across all cell cycle states, representing no direct regulation of protein synthesis/ degradation/ signaling by cell cycle processes. View this table: View inline View popup Table 1: Estimation of values of the model parameters We set up a Master equation 28 to describe the stochastic kinetics involving the cell signaling and cell cycle transitions as described above. The Master equation was then employed to analytically evaluate the kinetics of population-averaged protein abundances in each cell cycle stage (details in the Supplementary Text 1 , sections 1-4). In parallel, we developed a stochastic simulation approach to numerically simulate the stochastic trajectories of single-cell abundances of A and A* as the cells progress through cell cycle stages. The details regarding the algorithm are provided in the Materials and Methods section. In the model, the total number of cells increases continuously with time due to cell division; however, the population-averaged number of cells in any given cell cycle state β relative to the total number of cells across all cell stages, denoted by ρ β (see in Materials and Methods), reaches a stationary state after a sufficiently long period. The time evolution of ρ β for the states β =1 to N in the model is described by a set of coupled non-linear ordinary differential equations (ODEs) ( Supplementary Text 1 , section 5) The above non-linear ODEs can be solved numerically. We compared the numerical solutions of the ODEs with the numerical simulations of the stochastic kinetics, which showed excellent agreement ( Figure 3C ). The steady states of the above ODEs can be analyzed analytically. The steady state of the above kinetics (see Materials and Methods section) shows that the longer the duration of a cell cycle state, the larger the fraction of cells residing in that state ( Supplementary Text 1 , section 6). The kinetics of the population-averaged abundance of the total amount of protein A = A U + A* (= a β ) and phosphoprotein in any given cell cycle state β depends on the rates ( θ β ) of synthesis, degradation, phosphorylation, and de-phosphorylation in state β, as well as on the cell cycle transition rate from β − 1 → β, and the fraction of the cells in both the previous state (β-1 for β >1, and, N for β =1) and the current (state β) cell cycle state. The kinetics of a β ( Supplementary Text 1 , section 5) is given by, and the kinetics of with full heritability of a* is given by, Where . Here, the rates of protein synthesis, degradation, phosphorylation, and dephosphorylation are denoted by and , respectively, in state β. The above system of non-linear ODEs can be solved numerically, and the steady-state behavior can be analyzed analytically (see Materials and Methods, Supplementary Text 1 , section 5). The numerical solution of the above ODEs showed excellent agreement with our stochastic simulations ( Figure 3D ). Below, we describe the dependencies of the steady-state average abundances of A and A* on the kinetic rates pertaining to the cell cycle, protein synthesis and degradation, and phosphorylation and dephosphorylation processes. In the absence of any cell cycle transitions, the steady-state value of a is fully determined by the synthesis and degradation rates r and δ , respectively, i . e ., ( Supplementary Text 1 , section 9). In the presence of cell cycle transitions, the steady state average abundance a β depends on the synthesis and degradation rates r (β) and δ (β) , as well as on the steady state values of the average per-cell abundances of A in the preceding cell cycle state with a weight factor < 1 (see Materials and Methods, Supplementary Text 1 , section 5, Eqn. 57). We can make few general observations from our analysis of the steady state of a . (i) Neutral case: For protein synthesis and degradation rates that do not change with cell cycle states, i.e., r ( β ) = r and δ ( β ) = δ , the average abundance per cell a β increases monotonically as the cell progresses through the cell cycle states when the protein degradation rate δ is slower than the cell cycle transition rates k β . However, when the rates of protein synthesis and degradation are substantially larger than the cell cycle transition rates, i.e., δ ≫ k β , the average protein abundances per cell a β are roughly equal in all cell cycle states in this case. (ii) Active case: When the rates r and δ depend on the cell cycle states, there can be non-monotonic changes in the steady state-values of a β with progressing cell cycle states. Next, we analyzed the average abundances of the phosphorylated protein species A in the steady state. Using similar arguments as for { a β } we can make the following general observations. 1. Neutral case When the protein synthesis/degradation and phosphorylation/dephosphorylation rates do not change with cell cycle stages, i.e., , and, increases monotonically as the cell progresses through the cell cycle when the protein degradation rate δ is slower than the cell cycle transition rates k β , tracking the increase in a β as the cells advance. If a β remains unchanged with cell cycle stages, also remains unchanged. 2. Active case Any decrease or non-monotonic change in results from cell cycle-dependent rates of protein synthesis/degradation and/or phosphorylation/dephosphorylation. Therefore, any decrease or non-monotonic change in the average abundance of phosphorylated protein results from changes in protein synthesis/ degradation rates and/or phosphorylation/ dephosphorylation rates, which are influenced by cell cycle states. These variations in the rates could involve direct participation of proteins (e.g., CDKs) that regulate cell cycle transitions. In the next section, we investigate coupling of a basic non-linear biochemical signaling reaction with cell cycle processes. The model cannot be solved analytically; therefore, we use stochastic simulations of the model for our investigation. Modeling coupling of non-linear biochemical signaling reactions with cell cycle processes We considered phosphorylation of a substrate protein species A (e.g., Vav1) by a kinase E (e.g., Src kinase), where the kinase binds to the substrate via a second-order reaction and then phosphorylates it ( Figure 4A ). The phosphorylated substrate A* is dephosphorylated by phosphatases, which is modeled as a first-order reaction. The above reactions are common in many NK cell receptors including NKG2D receptor-initiated signaling. Because the propensity of a second-order reaction, which determines how frequently the reaction occurs, decreases with increasing cell volume (V) as ∝ 1/V, we considered the increase in the volume of a single cell in our stochastic simulation as it progresses through the cell cycle. We also considered for the production and degradation of the substrate A, and the kinase E in the different cell cycle stages, which are modeled by zero- and first-order reactions. The changes in the abundances of A, A*, E, and the intermediate complexes EA as cells transition through cell cycle stages are modeled in the same way as described in the previous section. Further details are provided in the Materials and Methods section. Download figure Open in new tab Figure 4: Kinetics of average protein abundances in cells residing in different cell cycle stages for a non-linear signaling reaction model. (A) Schematic representation of a non-linear signaling reaction model. Enzyme E and its substrate A bind to form a complex C, that gives rise to phosphorylated protein A* and the enzyme E is released. The proteins A, E, C and A* can be degraded, and the proteins A and E are produced in the cell with zeroth-order reactions. Rates associated with the reactions are shown above arrows. (B-D) Shows the average abundances of A* at the steady state for the signaling model in (A) at cell cycle stages G1, S, G2, and M. The results are shown for the neutral ( B and C ) and the active (D) scenarios. The neutral case can give rise to monotonic increase (B) , non-monotonic change ( C , left panel), and monotonic decay ( C , right panel) in the average abundance of A* for G1 → S → G2. The non-monotonic change ( C , left) or the monotonic decay ( C , right) can be observed in the neutral case within a narrow parameter range. In the active case the rate of protein phosphorylation is decreased 100-fold in S stage ( D , left) which produces a non-monotonic change (decrease, increase) for G1 → S → G2 in the average abundance of A*. Increasing the rate of phosphorylation of A* 100 times in S stage and reducing it 100 times in G2 and M stages generates another type of non-monotonic change (increase, decrease) with progressing cell cycle stages for G1 → S → G2 ( D , right). For B-D , the mean and the standard error of the mean (SEM) of the average abundance of A* are calculated from 20 simulation replicates. Asterisks represent the statistical significance in t- test with P -value < 0.05 which we calculated independently between G1 and S stage, S and G2 stage, and G2 and M stages with n = 20 samples of the average abundance of A* in each cell stage. Parameter values used and P -values calculated from t- tests in B-D are provided in Supplementary Table S2 . We then simulated the above reactions shown in Figure 4A to evaluate the variation of the cell population-averaged abundances of across cell cycle stages and the underlying mechanisms. We investigated both the neutral and the active scenarios as described previously for the first-order signaling model, where the rates of protein synthesis, degradation and the rates for biochemical signaling reactions (i.e., phosphorylation/dephosphorylation/association/dissociation) are neutral or depend actively on cell cycle states. We observed the following patterns in the variations of the per cell average abundances in steady state as cells progress through cell cycle states (details in Supplementary Text 1 , section 11 and Supplementary Table S3 ). (a) Monotonic increase In the neutral case, the average abundance of increases from G1→ S → G2 + M when the time scales for protein degradation (∝ 1/ δ ) is similar or larger than that of the cell cycle transition time scales, i.e., 1/ δ ≥ {1/ k β }. In this situation, the total abundances of the substrate, intermediate complex and product (A total = A + A* + EA), and the enzyme (E total = E + EA) increase as the cell progresses through cycle states, with each cell cycle state accumulating the abundances from previous state. Consequently, as the substrate and the enzyme abundances increase, this leads to greater abundances of A* in successive cell cycle stages compared to the previous one ( Figure 4B ). In the active case, we can achieve this behavior for a wider range of rate parameters, e.g., when the rates of protein synthesis/phosphorylation increase with increasing cell cycle states, the kinetics can generate a monotonic increase regardless of the degradation rate. (b) Monotonic decrease This pattern occurs in the neutral case when the rate of protein degradation is much faster compared to the cell cycle transitions ( δ ≫{ k β }). In this scenario, the average per cell abundances of A total and E total reach a steady state at each cell cycle state, and thus do not vary across cell cycle states. However, as the cell volume increases with cell cycle progression, the propensity for the second-order reaction producing the intermediate complex, EA, decreases, leading to the decrease of the abundance of A* ( Figure 4C ). For the cell volume increases by a factor of approximately two before division, the monotonic decrease in the abundance of A* observed in Figure 4C is ~ 0.23 fold across all cell cycle stages. This point is further considered in the Supplementary Text 1 , section 11. For the active case, a decrease (or increase) in the synthesis (or degradation) rate or a decrease (or increase) in protein phosphorylation (or dephosphorylation) rate with cell cycle progression can give rise to a substantially large monotonic decrease. (c) Non-monotonic changes This behavior can occur in the neutral case for a narrow range of parameter values within the ranges provided in Supplementary Table S1 . For instance, this situation can arise when the increase in the propensity of the second-order reaction (e.g., protein binding: E + A → EA) yielding the intermediate complex EA due to the increase in the total abundances of E (E total ) and A(A total ) with progressing cell cycle stages is counteracted by the decrease in propensity caused by the increasing cell volume (see Supplementary Text 1 , section 11 for further details). For specific values of r, δ, and the biochemical signaling rates, we can obtain an increasing abundance of A* from G1→ S, and then decrease from S → G2 + M ( Figure 4C ). However, the magnitudes of protein variation are small ~ 0.06 fold ( Figure 4C ) . The non-monotonic changes are more easily obtained in the active case by cells introducing cell cycle-dependent rates of protein synthesis, or degradation, or biochemical signaling rates ( Figure 4D ). (d) Unchanged abundances This behavior can be obtained in the neutral case when the degradation of E and A are faster compared to the cell cycle transitions ( δ ≫{ k β }) that leads to the constant per cell abundances of A* across cell cycle stages when cell volume does not change across these stages. When the growing cell volume is taken into consideration, a high binding affinity between the E and A (or low dissociation constant K D ) reduces the effect of increasing cell volume on the reaction propensity and consequently on the abundances of A*. As a result, the protein abundances remain unchanged across cell cycle stages ( Supplementary Text 1 , section 11, Supplementary Table S3 ). Similarly, in the active case, if the cell cycle dependencies of the synthesis/degradation/biochemical signaling rates are tuned such that those counteract the increases or decreases in abundances of A* between consecutive cell cycle stages obtained in either the active or the neutral case as described before. To quantify the proportion and robustness of different types of phosphoprotein variation (monotonic vs. non-monotonic) in the neutral scenario, we initially performed numerical simulations within a specific range of parameters (~ 20-30 fold variation in k on and δ , see Supplementary Table S2C ). These simulations resulted in ~26% non-monotonic cases and ~2% monotonic decrease cases, with the monotonic decay and non-monotonic variation being at most ~ 0.2 fold and ~ 0.1 fold, respectively. Furthermore, we developed approximate analytical expressions to estimate variations of the abundances with cell cycle states across parameter ranges. Details on the maximum variation in protein abundances in the neutral scenario are provided in Supplementary Text 1 , Section 11 ( Supplementary Figure S9) . Discussion NK cells proliferate in response to NKR and cytokine stimulations. As proliferating NK cells progress through cell cycle states from G1→ S→ G2→ M, many proteins including those involved in NKR and cytokine signaling, are synthesized acquiring different abundances in each cell cycle state. In addition, physical characteristics of dividing cells, such the cell volume that can affect the propensity of signaling reactions and the abundances of signaling products increase with cell cycle progression. Our investigation of the variations in the abundances of NKG2D signaling proteins with cell cycle states, using CyTOF experiments in IL-2-treated primary CD56 dim NK cells showed monotonic or semi-monotonic increases, non-monotonic changes, and no-changes in the population-averaged per cell abundances of phosphorylated signaling proteins with progressing cell cycle states. The majority (~ 89%) of the 31 measured proteins (e.g., CD107a, pCrkL, and pPLCγ2) at various timepoints in the NKG2D-stimulated primary CD56 dim NK cells showed monotonic or semi-monotonic increases. Whereas a small proportion (~ 9%) of the proteins, such as pVav1 and pNFκB, exhibited non-monotonic changes at specific time points during NKG2D signaling. NKG2D stimulation of human NKL cells constitutively expressing NKG2D receptor by plate-bound antibodies showed a higher proportion (~15%) of the proteins showing non-monotonic changes such as CD69 and pS6. The abundances of these proteins show a higher frequency of semi-monotonic behavior in primary NK cells compared to NKL cells. Although the fraction of cells expressing high abundances of CD107a was larger in NKL cells compared to primary NK cells ( Supplementary Figure S6 ), the variation in CD107a abundances with cell cycle stages was qualitatively similar between NKG2D stimulated primary NK cells and NKL cells. For Ly49H-stimulated NKL cells, the proportions of non-monotonic changes increased (~17%) compared to the primary NK cells; CD107a or CD69 abundances showed no changes across cell cycle stages in contrast to NKG2D-stimulated NKL cells. The increased instances of non-monotonic changes as well as differences in cell cycle dependence of particular signaling proteins (e.g., pS6) in the NKL cells suggest increased influence of cell cycle driving proteins on NK cell signaling kinetics. In addition, the specific proteins that show qualitative differences in changes in protein abundances with cell cycle stages in primary CD56 dim NK cells post-NKG2D stimulation and the NKL cells post-Ly49H stimulation, which could potentially be due to differences in NKR signaling (e.g., DAP10 versus DAP12 adapter signaling). We explored mechanisms that can make the NK cell signaling kinetics dependent on cell cycle states, specifically, when the time scales for cell cycle transition are about an order of magnitude longer than those of the signaling kinetics. To investigate this, we developed minimal models that can describe enzymatic chemical modifications (e.g., phosphorylation or dephosphorylation) of signaling proteins. Using both analytical calculations and simulations, we examined the coupling of biochemical signaling kinetics and the physiochemical changes that are associated with cell cycle transitions. Our analyses for the neutral case revealed that when the degradation rates of enzyme (e.g., kinase and phosphatases) are much smaller than the cell cycle transition rates, the abundances of the phosphorylated forms of the substrate increased monotonically as the cell cycle progresses following the increase in the abundance of enzyme and substrate. In contrast, when protein degradation rates exceed cell cycle transition rates, the changes in the abundances of the phosphorylated signaling protein (product) with cell cycle progression is negligible if the cell volume remains unchanged with cell cycle progression. However, as the cell volume approximately doubles during cell cycle progression, the rate of binding of the enzyme and the substrate effectively decreases by a factor of approximately two with cell cycle stages resulting in the decrease of the abundance of the phosphoprotein. This can lead to a monotonic decay (decrease-decrease) in the abundance of the phosphorylated substrate. In the situation when the degradation rates are comparable to the cell cycle transition rates, the abundances of the enzyme and substrate increase progressively with cell cycle transition. This can overcome for the effective decrease in the rate of binding by the volume increase for limited range of parameter values (see Supplementary Table S2 ) and lead to an increase in the abundance of the phosphoprotein. A non-monotonic variation (e.g., increase-decrease) in the abundance of the phosphoprotein can arise when the above compensation takes place for G1→ S but not for S → G2. Our modeling within a specific parameter range ( Supplementary Table S2C ) showed that such non-monotonic protein variation occurs in about 26% of cases, indicating that it less likely to occur in nature compared to monotonic or semi-monotonic protein variation cases. In contrast, for the active case, we found that the active influence of cell cycle regulating proteins generate non-monotonic variations in phosphoproteins in NK cell signaling for a wide range of parameters and variations of the proteins across cell cycle stages are much larger (~ several folds). Thus, the presence of such non-monotonicity is likely to indicate active modulation of signaling kinetics by cell cycle processes. The time scale NK cell proliferation is about an order of magnitude slower than that (~ 1/mins to 1/secs) of the signaling kinetics – thus the signaling kinetics in a cell cycle state was mainly influenced by the protein synthesis and degradation rates in the cell cycle state. However, for lymphocytes such as T cells, the cell division can occur in much shorter (~ 2-4 hours duplication time 41 ) time scale in the expansion phase. In such cases the cell cycle transition and signaling kinetic time scales can be less separated in magnitude, and the protein synthesis/degradation rates as well as the abundances of phosphorylated forms of the proteins in several preceding states can influence the signaling kinetics in the current state. This will be an interesting future direction. We analyzed simple enzymatic signaling reactions in our model. However, certain signaling reactions can involve positive feedbacks where the product promotes its own production and display digital response to stimulations, e.g., Ras activation in T- and B-cells showing a digital response depending on abundances of RasGEFs such as SOS1 and Rasgrp1 42 . As the abundances of substrates and enzymes can vary across cell cycle states, it would of interest to investigate if such digital response occurs in specific cell cycle states. The limitation of the study For primary NK cells, expressions of some of the cell cycle marker proteins (e.g., pH3) were low which made it difficult for us to separate G2 and M stages in gating the cell populations using UMAP embeddings. We manually gated cell populations into different cell cycle stages on the UMAP plane, which resulted in the loss of a small fraction of cell population at the borders between two cell cycle gates. In addition, some the proteins and the timepoints where non-monotonic (or monotonic) changes with progressing cell cycles occurred showed dependence on the choice of the parameters used in CyTOF data analysis (see Materials and Methods and Supplementary Figure S7 ). Thus, confirmation of the underlying mechanisms regarding the cell cycle dependence of the protein abundances requires further experimental validation. We considered four cell cycle stages in simulating the non-linear signaling kinetics to keep the computation time feasible. This makes the duration of the cell cycle states in the model distributed exponentially; however, the durations of cell cycle states have been observed to follow an Erlang distribution with substantially less variations than the exponential distribution. Since the cell cycle durations are almost an order of magnitude longer than the cell signaling time scales, we reasoned the variations in the durations caused by the exponential distributions will not affect the qualitative conclusions drawn from the model. Materials and Methods Cell preparation and NKR stimulation Human peripheral blood NK cells were isolated from blood obtained from healthy adult donors, cultured in IL-2 for 24 hours, and then stimulated with plate-bound agonist anti-human NKG2D mAb as described previously 43 . The IL-2-treated NK cells were stimulated with anti-human NKG2D mAb (5 µg/ml, clone 1D11, BioLegend) for 2, 4, 8, 16, 32, 64, and 256 min. The NKL cells used in this study were generated and maintained as described previously 44 . The human NKL cell line, which endogenously expresses NKG2D, was transduced with pMX-puro retroviral vectors containing the mouse Ly49H and positive NKL cells were isolated by using flow cytometry sorting 8 . The NKL cells were stimulated with plate-bound agonist anti-Ly49H (5 µg/ml, clone 3D10, eBioscience) mAbs) or anti-NKG2D (5 µg/ml, clone 1D11, Biolegend) mAbs as described previously 44 for 8, 32, 64, 128, and 256 min. Mass cytometry Cell staining and mass cytometry (i.e., CyTOF) was performed as described previously 43 . The mass cytometry Ab panels used for the analysis of primary human NK cells and NKL cells are shown in Supplementary Table S4 and Table S5 , respectively. Gating strategy Gating of live CD56 dim NK cells (i.e., CD45 + cisplatin - CD3 - CD235 - CD61 - CD15 - CD56 dim CD16 + ) and live NKL cells (i.e., CD45 + cPARP - cisplatin - ) was done using Cytobank software. Gating of CD56 dim NK cell and NKL populations residing in different cell cycle stages was performed using UMAP (nearest neighbor = 15, min distance = 0.01) based on the cell cycle markers Idu, pRb, Cyclin B, pH3, and Ki67, and cell viability marker cisplatin in Cytobank software. We first eliminated dead cells by removing the cisplatin + pRb - Idu - pH3 - population. The cell population in the G0 stage was gated based on pRb - Idu - CyclinB1 low pH3 - expression ( Supplementary Figure S1 ). The cell populations in the G1, S, and G2 stages were gated based on pRb + Idu - CyclinB1 low pH3 - expression, Idu + pH3 - expression, and Idu - CyclinB1 high pH3 - expression, respectively ( Supplementary Figure S1 ). In NKG2D-stimulated primary NK cells, we did not see a clear distinction of the pH3 + expression; therefore, we could not separate the cell population in the M stage from the G2 stage and designated as G2-M stage. ( Supplementary Figure S1 ). Whereas in NKL cells, we identified distinct populations of M-stage cells that are pH3 + pS6 + pMAPKAPK2 +22 , although their percentage is very small. Here, we combined these two populations G2 and M into a single G2+M stage and similarly designated it as the G2-M stage. Data processing We exported the untransformed mass cytometry (.fcs) data after splitting it into cell cycle stages. Our gating yielded cell numbers that varied between ~ 400-900 for the G0, S, and G2-M stages and ~ 3000-4000 for the G1 stage. Next, we examined the distribution of intensities corresponding to the expression of signaling proteins in cell populations residing in different cell cycle stages at various time points. The distributions of intensities are asymmetric and contained expressions at negative values. To compare the protein behavior between cell cycle stages ( Figure 2E , Supplementary Figure S3 and S4 ) or compute the geometric mean of the protein expression ( Figure 2G , Supplementary Figure S2) we transformed the intensities to a natural log scale (log e ). We assigned a small constant value ϵ (10 -11 ), less than the minimum positive intensity (~10 - 5 ), to the negative and zero values as the logarithm of these values cannot be computed ( Supplementary Figure S5 ). We checked sensitivity of the protein variation with cell cycle states to the variation of ϵ and the significance level α used in the t -test for primary NK cells vs. NKL cells. The qualitative nature of the protein variations in Figure 2E did not change for ϵ <10 -11 , but changed at certain time points for those proteins when ϵ was chosen to be higher (~10 -9- 10 -6 ) (see Supplementary Figure S7 for details ) . In addition, decreasing to α < 0.05 led to qualitative changes in some protein variations compared to that shown in Figure 2E . Statistical tests To determine whether the log-transformed intensities of a signaling protein increased, decreased, or did not change between cell cycle stages ( Figure 2E , Supplementary Figure S3 and S4 ), we sorted single cells into cell cycle stages. We then performed a one-sided t- test comparing the log-transformed intensities of single cells between two cell cycle stages (e.g., G1 and S) to assess whether an increase occurred between the stages (H 1 : μ 2 > μ 1 ). We additionally performed a one-sided t- test to determine whether the protein expressions decreased between the cell cycle stages (H 1 : μ 2 < μ 1 ). If neither of these tests achieved the significance level α = 0.05, we classified the protein as having “no change” between the stages. For our stochastic simulation results presented in Figure 4 , we used similar t- tests to compare the phosphoprotein abundances at steady state between cell cycle stages. Kinetic equations for average cell populations and protein abundances We evaluated the kinetics of the total numbers of cells ( n β ) in any cell cycle state β , as well as the total numbers of A (or A β ) and A* (or ) in the cell population residing in the state β , using the Master equation 45 describing the stochastic kinetics for the transitions in Eqns. (5-7). The details of the derivation are provided in the Supplementary Text 1 (sections 1-4). Here, we present the ODEs describing the above kinetics which show the couplings between the processes regulating the cell cycle and phosphorylation/dephosphorylation kinetics. The kinetics for {n β } are described by, The kinetics for A β are given by, The kinetics for when there is no heritibility of A* during cell division are given by, For the case of full heritibility , the kinetics of for β ≥ 2 is same as that above, and for β =1 it is changed to, In CyTOF experiments, single cells can be sorted based on expression levels of specific proteins to determine the cell cycle state that single cell is residing in. Abundances of different protein species can be then evaluated in these sorted cells. However, cytometry experiments do not track changes in the total number of cells that can occur due to cell division. Therefore, the relative numbers of cells in different cell cycle states, i.e., ρ β = n β /(∑ β n β ), and the average abundance of protein species A in a cell cycle state β, given by a β = A β / n β , can be evaluated from the CyTOF data. The number of cells in each cell cycle state, {n β }, increase exponentially with time, therefore, the total number of proteins in the cell population, { A β } and, increase exponentially with time as well. However, the relative numbers of cells in any state β, given by approaches a steady state. The kinetics of {ρ β }is given by (see Supplementary Text 1 , section 5.1 for details), The steady state values are given by, The average abundances of A and A* in a single cell { a β } and { a * β }, respectively, approach steady states as well. The kinetics of these variables are given by (see Supplementary Text 1 , section 5.2 for details), and, For no heritability the equations for are (see Supplementary Text 1 , section 5.3 for details), For full heritability for are, Here, for 1≤ β ≤ N. The steady state values of { a β } as functions of the scaled and dimensionless (i.e., ≤ 1) variables are given by (see Supplementary Text 1 , section 5.2 for details), and, where, The steady state values for functions of dimensionless and variables are given by (see Supplementary Text 1 , section 5.3 for details), for 2 ≤ β ≤ N, where, Stochastic simulations Multi-scale stochastic simulations were performed in MATLAB. The code can be found at https://github.com/indraniny/NK_cell_cycle_and_signaling , and a descriptive illustration is provided in Supplementary Figure S8 . The simulation was seeded with 400 cells for the linear model (or 20 cells for the non-linear model), initialized with the abundances of each protein and a cell cycle stage designation. See “Initial Condition Generation” in Methods for details. Then, for each cell, a Gillespie simulation is performed 46 , where the cell can perform any protein-level reaction, or progress to the next stage of cell cycle. If the cell reaches the final stage (i.e. M stage) and advances, it divides, generating a second daughter cell. Proteins from the parent cell are randomly split between the two daughter cells according to a binomial distribution. Each cell also retains the “time” advanced from the previous timesteps in the Gillespie simulation for that cell. The process continues, with each cell independently selecting reactions to perform via the Gillespie simulation. When a cell is about to complete a reaction that would advance it past the endpoint time of interest, it is removed from the simulation and placed in the output. The simulation continues until all cells have been removed. The resulting output is a collection of cells that would be observed at the endpoint time of interest, originating from the input cells. Finally, we calculated the average behavior of protein abundances from the collections of cells obtained at the endpoint time for each cell cycle stage. For non-linear simulations that require a volume correction (i.e., for a second-order reaction that governs binding of two proteins), the propensity for the reaction to occur decreases as the volume increases, which is correlated with progression through the cell cycle. To account for this, we assume that the propensity of the reaction to occur in each stage is given by: Where V i = 1, 1.3, 1.6, 2.0 represents the volume factors in G1, S, G2, and M, respectively. This allows the volumes of each stage to take values between initial volume and twice the initial volume, mimicking a monotonic increase in cell volume up to a doubling of the cell volume. The simulations for the linear model, shown in Figure 3 , took approximately one hour. The simulations for the non-linear model, which produced the results shown in Figure 4 , had runtimes ranging from approximately 1 to 35 hours. Initial Condition Generation For the non-linear model, we began with a population of 20 cells, each containing 80 molecules of the enzyme (E) and 80 molecules of the substrate (A) ( Supplementary Tables S1 and S2 ). Initially, all cells were assumed to be in the G1 state of the cell cycle. Over time, these cells progress through the subsequent stages—S state, G2 state, and M state —before undergoing division to produce two daughter cells. The signaling pathway involves the binding of the enzyme (E) to the substrate (A), forming a complex (EA) that is further phosphorylated to create the product (A*), as described in Figure 4A (details in results section).We then let the system of reactions run for a long period (~ 5 generations of cells or 170 hours) until the mean protein concentrations of all species achieve steady state. At this point, we calculated the average protein abundances per cell at cell cycle stages G1, S, G2, and M. Because stage M has the shortest duration (~ 1.4 h), the number of cells in this stage is relatively low. In contrast, stage G1 has the longest duration, resulting in a higher number of cells (~14 h) ( Supplementary Table S1 and S2) . Consequently, the fluctuation in average protein abundance is more pronounced during stage M, while it is less variable in the G1 state. We independently ran 20 simulation replicates of identical initial configurations to calculate the standard error of average protein abundance (SEM) in Figures 4B-D . Metric for Protein variation in sensitivity analysis To quantify protein variation across cell cycle stages, we used the formula: (max−min)/min for fold change. Where max and min represent the average protein abundance per cell across the G1, S, G2, and M stages. Code Availability The codes for this manuscript are written in MATLAB and Python, can be accessed https://github.com/indraniny/NK_cell_cycle_and_signaling . Author Contributions Darren Wethington: Data processing; computational methods, investigation, data analysis; Figures; writing – original draft. Indrani Nayak: Data processing; computational methods, investigation, data analysis; Figures; writing – original draft. Helle Jensen: CyTOF experiments, Data curation, data analysis. Oscar A. Aguilar: Review. Gregory K. Behbehani: methodology, review. Lewis L. Lanier: Conceptualization, funding acquisition; investigation; methodology; project administration; supervision; writing – original draft, review and editing. Jayajit Das: Conceptualization, funding acquisition; investigation; methodology; project administration; supervision; Figures; writing – original draft, review and editing. Data Availability Statement CyTOF data are available from the corresponding authors upon request, except for identifying donor information. Acknowledgements This work was supported by NIH grant R01AI146581 to J.D. and NIH S10 Instrumentation Grant S10 1S10OD018040-01 to L.L.L. We acknowledge to Cytobank software for performing CyTOF data analysis. We thank to HPC facility Franklin at the Nationwide Children’s Hospital for providing computational resources. We acknowledge Ohio Supercomputer Center for usage of MATLAB. BioRender is used to create the schematic figures. References ↵ Lanier , L. L. Up on the tightrope: natural killer cell activation and inhibition . Nature immunology 9 , 495 – 502 ( 2008 ). OpenUrl CrossRef PubMed Web of Science ↵ Long , E. O. , Sik Kim , H. , Liu , D. , Peterson , M. E. & Rajagopalan , S. Controlling natural killer cell responses: integration of signals for activation and inhibition . Annual review of immunology 31 , 227 – 258 ( 2013 ). OpenUrl CrossRef PubMed Web of Science ↵ Abel , A. M. , Yang , C. , Thakar , M. S. & Malarkannan , S. Natural killer cells: development, maturation, and clinical utilization . Frontiers in immunology 9 , 1869 ( 2018 ). OpenUrl CrossRef PubMed ↵ Mesecke , S. , Urlaub , D. , Busch , H. , Eils , R. & Watzl , C. Integration of activating and inhibitory receptor signaling by regulated phosphorylation of Vav1 in immune cells . Science signaling 4 , ra36 – ra36 ( 2011 ). OpenUrl Abstract / FREE Full Text ↵ Grewal , R. K. & Das , J. Spatially resolved in silico modeling of NKG2D signaling kinetics suggests a key role of NKG2D and Vav1 Co-clustering in generating natural killer cell activation . PLoS Computational Biology 18 , e1010114 ( 2022 ). OpenUrl CrossRef ↵ Millan , A. J. et al. Spleen Tyrosine Kinase (SYK) negatively regulates ITAM-mediated human NK cell signaling and CD19-CAR NK cell efficacy . bioRxiv ( 2024 ). ↵ Milo , R. , Jorgensen , P. , Moran , U. , Weber , G. & Springer , M. BioNumbers—the database of key numbers in molecular and cell biology . Nucleic acids research 38 , D750 – D753 ( 2010 ). OpenUrl CrossRef PubMed Web of Science ↵ Robertson , M. et al. Characterization of a cell line, NKL, derived from an aggressive human natural killer cell leukemia . Experimental hematology 24 , 406 – 415 ( 1996 ). OpenUrl PubMed Web of Science ↵ Alberts , B. et al. Essential cell biology . ( Garland Science , 2015 ). ↵ Wu , J. et al. An activating immunoreceptor complex formed by NKG2D and DAP10 . Science 285 , 730 – 732 ( 1999 ). OpenUrl Abstract / FREE Full Text ↵ Upshaw , J. L. et al. NKG2D-mediated signaling requires a DAP10-bound Grb2-Vav1 intermediate and phosphatidylinositol-3-kinase in human natural killer cells . Nature immunology 7 , 524 – 532 ( 2006 ). OpenUrl CrossRef PubMed Web of Science ↵ Lanier , L. L. NKG2D receptor and its ligands in host defense . Cancer immunology research 3 , 575 – 582 ( 2015 ). OpenUrl Abstract / FREE Full Text ↵ Raulet , D. H. , Gasser , S. , Gowen , B. G. , Deng , W. & Jung , H. Regulation of ligands for the NKG2D activating receptor . Annual review of immunology 31 , 413 – 441 ( 2013 ). OpenUrl CrossRef PubMed Web of Science ↵ Spolski , R. , Li , P. & Leonard , W. J. Biology and regulation of IL-2: from molecular mechanisms to human therapy . Nature Reviews Immunology 18 , 648 – 659 ( 2018 ). OpenUrl CrossRef PubMed ↵ Alber , A. B. , Paquet , E. R. , Biserni , M. , Naef , F. & Suter , D. M. Single live cell monitoring of protein turnover reveals intercellular variability and cell-cycle dependence of degradation rates . Molecular cell 71 , 1079 - 1091 . e1079 ( 2018 ). OpenUrl CrossRef PubMed ↵ Herr , P. et al. Cell cycle profiling reveals protein oscillation, phosphorylation, and localization dynamics . Molecular & Cellular Proteomics 19 , 608 – 623 ( 2020 ). OpenUrl CrossRef PubMed ↵ Morgan , D. O. Cyclin-dependent kinases: engines, clocks, and microprocessors . Annual review of cell and developmental biology 13 , 261 – 291 ( 1997 ). OpenUrl CrossRef PubMed Web of Science ↵ Davidson , G. & Niehrs , C. Emerging links between CDK cell cycle regulators and Wnt signaling . Trends in cell biology 20 , 453 – 460 ( 2010 ). OpenUrl CrossRef PubMed Web of Science ↵ Liu , P. et al. Cell-cycle-regulated activation of Akt kinase by phosphorylation at its carboxyl terminus . Nature 508 , 541 – 545 ( 2014 ). OpenUrl CrossRef PubMed ↵ Behbehani , G. K. , Bendall , S. C. , Clutter , M. R. , Fantl , W. J. & Nolan , G. P. Single-cell mass cytometry adapted to measurements of the cell cycle . Cytometry Part A 81 , 552 – 566 ( 2012 ). OpenUrl Corneau , A. et al. Comprehensive mass cytometry analysis of cell cycle, activation, and coinhibitory receptors expression in CD4 T cells from healthy and HIV-infected individuals . Cytometry Part B: Clinical Cytometry 92 , 21 – 32 ( 2017 ). OpenUrl CrossRef PubMed Behbehani , G. K. Cell cycle analysis by mass cytometry . Cellular quiescence: Methods and protocols , 105 – 124 ( 2018 ). ↵ Hartmann , F. J. et al. Single-cell metabolic profiling of human cytotoxic T cells . Nature biotechnology 39 , 186 – 197 ( 2021 ). OpenUrl CrossRef PubMed ↵ Rapsomaniki , M. A. et al. CellCycleTRACER accounts for cell cycle and volume in mass cytometry data . Nature communications 9 , 632 ( 2018 ). OpenUrl CrossRef PubMed ↵ Mukherjee , S. et al. In silico modeling identifies CD45 as a regulator of IL-2 synergy in the NKG2D-mediated activation of immature human NK cells . Sci Signal 10 , doi: 10.1126/scisignal.aai9062 ( 2017 ). OpenUrl Abstract / FREE Full Text ↵ Smith , K. M. , Wu , J. , Bakker , A. B. , Phillips , J. H. & Lanier , L. L. Cutting edge: Ly-49D and Ly-49H associate with mouse DAP12 and form activating receptors . The Journal of Immunology 161 , 7 – 10 ( 1998 ). OpenUrl CrossRef PubMed ↵ Salazar , C. & Hofer , T. Kinetic models of phosphorylation cycles: a systematic approach using the rapid-equilibrium approximation for protein-protein interactions . Biosystems 83 , 195 – 206 , doi: 10.1016/j.biosystems.2005.05.015 ( 2006 ). OpenUrl CrossRef PubMed Web of Science ↵ Gardiner , C. W. Handbook of stochastic methods . Vol. 3 ( springer Berlin , 1985 ). ↵ Chao , H. X. et al. Evidence that the human cell cycle is a series of uncoupled, memoryless phases . Molecular systems biology 15 , e8604 ( 2019 ). OpenUrl Abstract / FREE Full Text ↵ Vittadello , S. T. , McCue , S. W. , Gunasingh , G. , Haass , N. K. & Simpson , M. J. Mathematical models incorporating a multi-stage cell cycle replicate normally-hidden inherent synchronization in cell proliferation . J R Soc Interface 16 , 20190382 , doi: 10.1098/rsif.2019.0382 ( 2019 ). OpenUrl CrossRef PubMed Yates , C. A. , Ford , M. J. & Mort , R. L. A Multi-stage Representation of Cell Proliferation as a Markov Process . Bull Math Biol 79 , 2905 – 2928 , doi: 10.1007/s11538-017-0356-4 ( 2017 ). OpenUrl CrossRef ↵ Perez-Carrasco , R. , Beentjes , C. & Grima , R. Effects of cell cycle variability on lineage and population measurements of messenger RNA abundance . Journal of the Royal Society Interface 17 , 20200360 ( 2020 ). OpenUrl CrossRef PubMed ↵ Golding , I. , Paulsson , J. , Zawilski , S. M. & Cox , E. C. Real-time kinetics of gene activity in individual bacteria . Cell 123 , 1025 – 1036 ( 2005 ). OpenUrl CrossRef PubMed Web of Science ↵ Huh , D. & Paulsson , J. Random partitioning of molecules at cell division . Proc Natl Acad Sci U S A 108 , 15004 – 15009 , doi: 10.1073/pnas.1013171108 ( 2011 ). OpenUrl Abstract / FREE Full Text ↵ Chatterjee , M. & Acar , M. Heritable stress response dynamics revealed by single-cell genealogy . Sci Adv 4 , e1701775 , doi: 10.1126/sciadv.1701775 ( 2018 ). OpenUrl FREE Full Text ↵ Chylek , L. A. et al. Phosphorylation site dynamics of early T-cell receptor signaling . PloS one 9 , e104240 ( 2014 ). OpenUrl CrossRef PubMed ↵ Hui , E. & Vale , R. D. In vitro membrane reconstitution of the T-cell receptor proximal signaling network . Nature structural & molecular biology 21 , 133 – 142 ( 2014 ). OpenUrl CrossRef PubMed ↵ Milo , R. & Phillips , R. Cell biology by the numbers . ( Garland Science , 2015 ). ↵ Schwanhäusser , B. et al. Global quantification of mammalian gene expression control . Nature 473 , 337 – 342 ( 2011 ). OpenUrl CrossRef PubMed Web of Science ↵ Trausch-Azar , J. , Leone , T. C. , Kelly , D. P. & Schwartz , A. L. Ubiquitin proteasome-dependent degradation of the transcriptional coactivator PGC-1α via the N-terminal pathway . Journal of Biological Chemistry 285 , 40192 – 40200 ( 2010 ). OpenUrl Abstract / FREE Full Text ↵ Lewis , D. A. & Ly , T. Cell cycle entry control in naïve and memory CD8+ T cells . Frontiers in Cell and Developmental Biology 9 , 727441 ( 2021 ). OpenUrl CrossRef ↵ Das , J. et al. Digital signaling and hysteresis characterize ras activation in lymphoid cells . Cell 136 , 337 – 351 ( 2009 ). OpenUrl CrossRef PubMed Web of Science ↵ Mukherjee , S. et al. In silico modeling identifies CD45 as a regulator of IL-2 synergy in the NKG2D-mediated activation of immature human NK cells . Science signaling 10 , eaai9062 ( 2017 ). OpenUrl Abstract / FREE Full Text ↵ Jensen , H. , Chen , S.-Y. , Folkersen , L. , Nolan , G. P. & Lanier , L. L. EBI3 regulates the NK cell response to mouse cytomegalovirus infection . Proceedings of the National Academy of Sciences 114 , 1625 – 1630 ( 2017 ). OpenUrl Abstract / FREE Full Text ↵ Gardiner , C. W. Handbook of stochastic methods-for physics, chemistry and the natural sciences . Springer series in synergetics 13 , 3 – 18 ( 1985 ). OpenUrl ↵ Gillespie , D. T. Exact Stochastic Simulation of Coupled Chemical Reactions . The Journal of Physical Chemistry 81 , 2340 – 2361 ( 1977 ). OpenUrl CrossRef PubMed Web of Science Liu , Y. et al. Growth and activation of natural killer cells ex vivo from children with neuroblastoma for adoptive cell therapy . Clinical Cancer Research 19 , 2132 – 2143 ( 2013 ). OpenUrl Abstract / FREE Full Text Marchingo , J. M. & Cantrell , D. A. Protein synthesis, degradation, and energy metabolism in T cell immunity . Cellular & molecular immunology 19 , 303 – 315 ( 2022 ). OpenUrl CrossRef PubMed Wolf , T. et al. Dynamics in protein translation sustaining T cell preparedness . Nature immunology 21 , 927 – 937 ( 2020 ). OpenUrl CrossRef PubMed Eden , E. et al. Proteome half-life dynamics in living human cells . Science 331 , 764 – 768 , doi: 10.1126/science.1199784 ( 2011 ). OpenUrl Abstract / FREE Full Text Schreiber , G. , Haran , G. & Zhou , H.-X. Fundamental aspects of protein− protein association kinetics . Chemical reviews 109 , 839 – 860 ( 2009 ). OpenUrl CrossRef PubMed Web of Science Bu , J. Y. , Shaw , A. S. & Chan , A. C. Analysis of the interaction of ZAP-70 and syk protein-tyrosine kinases with the T-cell antigen receptor by plasmon resonance . Proceedings of the National Academy of Sciences 92 , 5106 – 5110 ( 1995 ). OpenUrl Abstract / FREE Full Text Clemens , L. et al. Determination of the molecular reach of the protein tyrosine phosphatase SHP-1 . Biophysical journal 120 , 2054 – 2066 ( 2021 ). OpenUrl CrossRef PubMed View the discussion thread. Back to top Previous Next Posted February 28, 2025. Download PDF Supplementary Material Email Thank you for your interest in spreading the word about bioRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. 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