Digital signaling and hysteresis characterize ras activation in lymphoid cells.

Activation of Ras proteins underlies functional decisions in diverse cell types. Two molecules, RasGRP and SOS, catalyze Ras activation in lymphocytes. Binding of active Ras to SOS' allosteric pocket markedly increases SOS' activity establishing a positive feedback loop for SOS-mediated Ras activation. Integrating in silico and in vitro studies, we demonstrate that digital signaling in lymphocytes (cells are "on" or "off") is predicated upon feedback regulation of SOS. SOS' feedback loop leads to hysteresis in the dose-response curve, which can enable a capacity to sustain Ras activation as stimuli are withdrawn and exhibit "memory" of past encounters with antigen. Ras activation via RasGRP alone is analog (graded increase in amplitude with stimulus). We describe how complementary analog (RasGRP) and digital (SOS) pathways act on Ras to efficiently convert analog input to digital output. Numerous predictions regarding the impact of our findings on lymphocyte function and development are noted.

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.

Natural Killer (NK) cells provide key resistance against viral infections and tumors. A diverse set of activating and inhibitory NK cell receptors (NKRs) interact with cognate ligands presented by target host cells, where integration of dueling signals initiated by the ligand-NKR interactions determines NK cell activation or tolerance. Imaging experiments over decades have shown micron and sub-micron scale spatial clustering of activating and inhibitory NKRs. The mechanistic roles of these clusters in affecting downstream signaling and activation are often unclear. To this end, we developed a predictive in silico framework by combining spatially resolved mechanistic agent based modeling, published TIRF imaging data, and parameter estimation to determine mechanisms by which formation and spatial movements of activating NKG2D microclusters affect early time NKG2D signaling kinetics in a human cell line NKL. We show co-clustering of NKG2D and the guanosine nucleotide exchange factor Vav1 in NKG2D microclusters plays a dominant role over ligand (ULBP3) rebinding in increasing production of phospho-Vav1(pVav1), an activation marker of early NKG2D signaling. The in silico model successfully predicts several scenarios of inhibition of NKG2D signaling and time course of NKG2D spatial clustering over a short (~3 min) interval. Modeling shows the presence of a spatial positive feedback relating formation and centripetal movements of NKG2D microclusters, and pVav1 production offers flexibility towards suppression of activating signals by inhibitory KIR ligands organized in inhomogeneous spatial patterns (e.g., a ring). Our in silico framework marks a major improvement in developing spatiotemporal signaling models with quantitatively estimated model parameters using imaging data.

Determining clinically relevant features in cytometry data using persistent homology.

Cytometry experiments yield high-dimensional point cloud data that is difficult to interpret manually. Boolean gating techniques coupled with comparisons of relative abundances of cellular subsets is the current standard for cytometry data analysis. However, this approach is unable to capture more subtle topological features hidden in data, especially if those features are further masked by data transforms or significant batch effects or donor-to-donor variations in clinical data. We present that persistent homology, a mathematical structure that summarizes the topological features, can distinguish different sources of data, such as from groups of healthy donors or patients, effectively. Analysis of publicly available cytometry data describing non-naïve CD8+ T cells in COVID-19 patients and healthy controls shows that systematic structural differences exist between single cell protein expressions in COVID-19 patients and healthy controls. We identify proteins of interest by a decision-tree based classifier, sample points randomly and compute persistence diagrams from these sampled points. The resulting persistence diagrams identify regions in cytometry datasets of varying density and identify protruded structures such as 'elbows'. We compute Wasserstein distances between these persistence diagrams for random pairs of healthy controls and COVID-19 patients and find that systematic structural differences exist between COVID-19 patients and healthy controls in the expression data for T-bet, Eomes, and Ki-67. Further analysis shows that expression of T-bet and Eomes are significantly downregulated in COVID-19 patient non-naïve CD8+ T cells compared to healthy controls. This counter-intuitive finding may indicate that canonical effector CD8+ T cells are less prevalent in COVID-19 patients than healthy controls. This method is applicable to any cytometry dataset for discovering novel insights through topological data analysis which may be difficult to ascertain otherwise with a standard gating strategy or existing bioinformatic tools.

NK cells: tuned by peptide?

Natural killer cells express multiple receptors for major histocompatibility complex (MHC) class I, including the killer cell immunoglobulin-like receptors (KIRs) and the C-type lectin-like CD94:NKG2 receptors. The KIR locus is extremely polymorphic, paralleling the diversity of its classical MHC class I ligands. Similarly, the conservation of the NKG2 family of receptors parallels the conservation of MHC-E, the ligand for CD94:NKG2A/C/E. Binding of both CD94:NKG2 heterodimers and KIR to their respective MHC class I ligand is peptide dependent, and despite the evolution of these receptors, they have retained the property of peptide selectivity. Such peptide selectivity affects these two systems in different ways. HLA-E binding non-inhibitory peptides augment inhibition at CD94:NKG2A, while HLA-C binding non-inhibitory peptides antagonize inhibition at KIR2DL2/3, implying that KIRs are specialized to respond positively to changes in peptide repertoire. Thus, while specific KIRs, such as KIR2DL3, are associated with beneficial outcomes from viral infections, viral peptides augment inhibition at CD94:NKGA. Conversely, NKG2A-positive NK cells sense MHC class I downregulation more efficiently than KIRs. Thus, these two receptor:ligand systems appear to have complementary functions in recognizing changes in MHC class I.

Defining pharyngeal contractile integral during high-resolution manometry in neonates: a neuromotor marker of pharyngeal vigor.

BACKGROUND: Pharyngeal contractility is critical for safe bolus propulsion. Pharyngeal contractile vigor can be measured by Pharyngeal Contractile Integral (PhCI): product of mean pharyngeal contractile amplitude, length, and duration. We characterized PhCI in neonates and examined the hypothesis that PhCI differs with mode of stimulation. METHODS: Nineteen neonates born at 38.6 (34-41) weeks gestation were evaluated at 42.9 (40.4-44.0) weeks postmenstrual age using high-resolution manometry (HRM). PhCI was calculated using: (a) Conventional and (b) Automated Swallow Detection algorithm (ASDA) methods. Contractility metrics of all pharyngeal regions were examined using mixed statistical models during spontaneous and adaptive state (pharyngeal and oral stimulus) swallowing. RESULTS: PhCI of oral stimuli swallows were distinct from pharyngeal stimuli and spontaneous swallows (P < 0.05). Correlation between conventional and ASDA methods was high (P < 0.001). PhCI increased with swallows for pharyngeal stimulation (P < 0.05) but remained stable for swallows with oral stimulation. PhCI differed between proximal and distal pharynx (P < 0.001). CONCLUSIONS: PhCI is a novel reliable metric capable of distinguishing (1) proximal and distal pharyngeal activity, (2) effects of oral and pharyngeal stimulation, and (3) effects of prolonged stimulation. Changes in pharyngeal contractility with maturation, disease, and therapies can be examined with PhCI.

Multiscale Modeling of Complex Formation and CD80 Depletion during Immune Synapse Development.

The mechanisms that discriminate self- and foreign antigen before T cell activation are unresolved. As part of the immune system's adaptive response to specific infections or neoplasms, antigen-presenting cells (APC) and effector T cells form transcellular molecular complexes. CTLA4 expression on regulatory or effector T cells reduces T cell activation. The CTLA4 transendocytosis hypothesis proposes that CTLA4 depletes CD80 and CD86 proteins from the APC membrane, rendering the APC incapable of activating T cells. We developed a multiscale spatiotemporal model for the interaction of a T cell and APC. Formation of the immune complex between T cell and APC starts with formation of the transmembrane complexes between the major histocompatibility complex and the T cell receptor (Signal 1) and between CD80 or CD86 and CD28 (Signal 2) at the opposing membrane surfaces of the interacting cells. By 0.01 s after contact simulation, an increasing concentration gradient of the free membrane proteins develops between the opposing surfaces and spherical parts of each cell's membrane, reaching a maximum at ∼30 s. Over several hours, diffusion across the gradient equalizes the free protein concentrations. During this phase, CTLA4 surface expression and its complexation with CD80/CD86 cause internalization and degradation of CD80/CD86. The simulation results show reasonable agreement with reported experimental data and indicate that key molecular processes take place over a very broad timescale, covering five orders of magnitude. Besides the fast complexation reactions, diffusion-limited processes, especially lateral diffusion in cell membranes and geometrical constraints, considerably slow down evolution of the synapse. Our results are consistent with the CTLA4 transendocytosis hypothesis and suggest the importance of lateral diffusion of surface proteins in contributing to a gradual increase in Signal 1 and Signal 2.

The balance between T cell receptor signaling and degradation at the center of the immunological synapse is determined by antigen quality.

The role of the center of the immunological synapse (the central supramolecular activation cluster or cSMAC) is controversial. One model suggests that the role of the cSMAC depends on antigen quality and can both enhance signaling and receptor downregulation, whereas a second model proposes that the sole function of the cSMAC is to downregulate signaling. An important distinction between the models is whether signaling occurs in the cSMAC. Here, we demonstrate that at early time points, signaling occurs outside the cSMAC, but occurs in the cSMAC at later time points. Additionally, we show that cSMAC formation enhances the stimulatory potency of weak agonists for the TCR. Combined with previous studies showing that cSMAC formation decreases the signaling by strong agonists, our data support a model proposing that signaling and receptor degradation both occur in the cSMAC and that the balance between signaling and degradation in the synapse is determined by antigen quality.

Limiting Energy Dissipation Induces Glassy Kinetics in Single-Cell High-Precision Responses.

Single cells often generate precise responses by involving dissipative out-of-thermodynamic-equilibrium processes in signaling networks. The available free energy to fuel these processes could become limited depending on the metabolic state of an individual cell. How does limiting dissipation affect the kinetics of high-precision responses in single cells? I address this question in the context of a kinetic proofreading scheme used in a simple model of early-time T cell signaling. Using exact analytical calculations and numerical simulations, I show that limiting dissipation qualitatively changes the kinetics in single cells marked by emergence of slow kinetics, large cell-to-cell variations of copy numbers, temporally correlated stochastic events (dynamic facilitation), and ergodicity breaking. Thus, constraints in energy dissipation, in addition to negatively affecting ligand discrimination in T cells, can create a fundamental difficulty in determining single-cell kinetics from cell-population results.

Peptide selectivity discriminates NK cells from KIR2DL2- and KIR2DL3-positive individuals.

Natural killer cells are controlled by peptide selective inhibitory receptors for MHC class I, including the killer cell immunoglobulin-like receptors (KIRs). Despite having similar ligands, KIR2DL2 and KIR2DL3 confer different levels of protection to infectious disease. To investigate how changes in peptide repertoire may differentially affect NK cell reactivity, NK cells from KIR2DL2 and KIR2DL3 homozygous donors were tested for activity against different combinations of strong inhibitory (VAPWNSFAL), weak inhibitory (VAPWNSRAL), and antagonist peptide (VAPWNSDAL). KIR2DL3-positive NK cells were more sensitive to changes in the peptide content of MHC class I than KIR2DL2-positive NK cells. These differences were observed for the weakly inhibitory peptide VAPWNSRAL in single peptide and double peptide experiments (p < 0.01 and p < 0.03, respectively). More significant differences were observed in experiments using all three peptides (p < 0.0001). Mathematical modeling of the experimental data demonstrated that VAPWNSRAL was dominant over VAPWNSFAL in distinguishing KIR2DL3- from KIR2DL2-positive donors. Donors with different KIR genotypes have different responses to changes in the peptide bound by MHC class I. Differences in the response to the peptide content of MHC class I may be one mechanism underlying the protective effects of different KIR genes against infectious disease.

Cell responses only partially shape cell-to-cell variations in protein abundances in Escherichia coli chemotaxis.

Cell-to-cell variations in protein abundance in clonal cell populations are ubiquitous in living systems. Because protein composition determines responses in individual cells, it stands to reason that the variations themselves are subject to selective pressures. However, the functional role of these cell-to-cell differences is not well understood. One way to tackle questions regarding relationships between form and function is to perturb the form (e.g., change the protein abundances) and observe the resulting changes in some function. Here, we take on the form-function relationship from the inverse perspective, asking instead what specific constraints on cell-to-cell variations in protein abundance are imposed by a given functional phenotype. We develop a maximum entropy-based approach to posing questions of this type and illustrate the method by application to the well-characterized chemotactic response in Escherichia coli. We find that full determination of observed cell-to-cell variations in protein abundances is not inherent in chemotaxis itself but, in fact, appears to be jointly imposed by the chemotaxis program in conjunction with other factors (e.g., the protein synthesis machinery and/or additional nonchemotactic cell functions, such as cell metabolism). These results illustrate the power of maximum entropy as a tool for the investigation of relationships between biological form and function.

Maximum Entropy Estimation of Probability Distribution of Variables in Higher Dimensions from Lower Dimensional Data.

A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n ≤ m, and the task is relatively straightforward for well-defined functional relationships. For example, if Y1 and Y2 are independent random variables, each uniform on [0, 1], one can determine the distribution of X = Y1 + Y2; here m = 2 and n = 1. However, biological and physical situations can arise where n > m and the functional relation Y→X is non-unique. In general, in the absence of additional information, there is no unique solution to Q in those cases. Nevertheless, one may still want to draw some inferences about Q. To this end, we propose a novel maximum entropy (MaxEnt) approach that estimates Q(x) based only on the available data, namely, P(y). The method has the additional advantage that one does not need to explicitly calculate the Lagrange multipliers. In this paper we develop the approach, for both discrete and continuous probability distributions, and demonstrate its validity. We give an intuitive justification as well, and we illustrate with examples.

Host-to-host variation of ecological interactions in polymicrobial infections.

Host-to-host variability with respect to interactions between microorganisms and multicellular hosts are commonly observed in infection and in homeostasis. However, the majority of mechanistic models used to analyze host-microorganism relationships, as well as most of the ecological theories proposed to explain coevolution of hosts and microbes, are based on averages across a host population. By assuming that observed variations are random and independent, these models overlook the role of differences between hosts. Here, we analyze mechanisms underlying host-to-host variations of bacterial infection kinetics, using the well characterized experimental infection model of polymicrobial otitis media (OM) in chinchillas, in combination with population dynamic models and a maximum entropy (MaxEnt) based inference scheme. We find that the nature of the interactions between bacterial species critically regulates host-to-host variations in these interactions. Surprisingly, seemingly unrelated phenomena, such as the efficiency of individual bacterial species in utilizing nutrients for growth, and the microbe-specific host immune response, can become interdependent in a host population. The latter finding suggests a potential mechanism that could lead to selection of specific strains of bacterial species during the coevolution of the host immune response and the bacterial species.

Impact of IL-21 on Natural Killer cell proliferation and function - a mathematical and functional assessment.

Natural killer (NK) cells are currently in use as immunotherapeutic agents for cancer. Many different cytokines are used to generate NK cells including IL-2, IL-12, IL-15 and IL-18 in solution and membrane bound IL-21. These cytokines drive NK cell activation through the integration of STAT and NF-κB pathways, which overlap and synergize, making it challenging to predict optimal cytokine combinations. We integrated functional assays for NK cells cultured in a variety of cytokine combinations with feature selection and mechanistic regression models. Our regression model successfully predicts NK cell proliferation for different cytokine combinations and indicates synergy between STAT3 and NF-κB transcription factors. Use of IL-21 in solution in the priming, but not post-priming phase of NK cell culture resulted in optimal NK cell proliferation, without compromising cytotoxicity or IFN-γ secretion against hepatocellular carcinoma cell lines. Our work provides a mathematical framework for interrogating NK cell activation for cancer immunotherapy.

Data-driven quantification of the robustness and sensitivity of cell signaling networks.

Robustness and sensitivity of responses generated by cell signaling networks has been associated with survival and evolvability of organisms. However, existing methods analyzing robustness and sensitivity of signaling networks ignore the experimentally observed cell-to-cell variations of protein abundances and cell functions or contain ad hoc assumptions. We propose and apply a data-driven maximum entropy based method to quantify robustness and sensitivity of Escherichia coli (E. coli) chemotaxis signaling network. Our analysis correctly rank orders different models of E. coli chemotaxis based on their robustness and suggests that parameters regulating cell signaling are evolutionary selected to vary in individual cells according to their abilities to perturb cell functions. Furthermore, predictions from our approach regarding distribution of protein abundances and properties of chemotactic responses in individual cells based on cell population averaged data are in excellent agreement with their experimental counterparts. Our approach is general and can be used to evaluate robustness as well as generate predictions of single cell properties based on population averaged experimental data in a wide range of cell signaling systems.

Positive feedback produces broad distributions in maximum activation attained within a narrow time window in stochastic biochemical reactions.

How do single cell fate decisions induced by activation of key signaling proteins above threshold concentrations within a time interval are affected by stochastic fluctuations in biochemical reactions? We address this question using minimal models of stochastic chemical reactions commonly found in cell signaling and gene regulatory systems. Employing exact solutions and semi-analytical methods we calculate distributions of the maximum value (N) of activated species concentrations (P(max)(N)) and the time (t) taken to reach the maximum value (P(max)(t)) within a time interval in the minimal models. We find, the presence of positive feedback interactions make P(max)(N) more spread out with a higher "peakedness" in P(max)(t). Thus positive feedback interactions may help single cells to respond sensitively to a stimulus when cell decision processes require upregulation of activated forms of key proteins to a threshold number within a time window.

PASCAR: a multiscale framework to explore the design space of constitutive and inducible CAR T cells.

CAR T cells are engineered to bind and destroy tumor cells by targeting overexpressed surface antigens. However, healthy cells expressing lower abundances of these antigens can also be lysed by CAR T cells. Various CAR T cell designs increase tumor cell elimination, whereas reducing damage to healthy cells. However, these efforts are costly and labor-intensive, constraining systematic exploration of potential hypotheses. We develop a protein abundance structured population dynamic model for CAR T cells (PASCAR), a framework that combines multiscale population dynamic models and multi-objective optimization approaches with data from cytometry and cytotoxicity assays to systematically explore the design space of constitutive and tunable CAR T cells. PASCAR can quantitatively describe in vitro and in vivo results for constitutive and inducible CAR T cells and can successfully predict experiments outside the training data. Our exploration of the CAR design space reveals that optimal CAR affinities in the intermediate range of dissociation constants effectively reduce healthy cell lysis, whereas maintaining high tumor cell-killing rates. Furthermore, our modeling offers guidance for optimizing CAR expressions in synthetic notch CAR T cells. PASCAR can be extended to other CAR immune cells.

McSNAC: A software to approximate first-order signaling networks from mass cytometry data.

Background: Mass cytometry (CyTOF) gives unprecedented opportunity to simultaneously measure up to 40 proteins in single cells, with a theoretical potential to reach 100 proteins. This high-dimensional single-cell information can be very useful in dissecting mechanisms of cellular activity. In particular, measuring abundances of signaling proteins like phospho-proteins can provide detailed information on the dynamics of single-cell signaling processes. However, computational analysis is required to reconstruct such networks with a mechanistic model. Methods: We propose our Mass cytometry Signaling Network Analysis Code (McSNAC), a new software capable of reconstructing signaling networks and estimating their kinetic parameters from CyTOF data. McSNAC approximates signaling networks as a network of first-order reactions between proteins. This assumption often breaks down as signaling reactions can involve binding and unbinding, enzymatic reactions, and other nonlinear constructions. Furthermore, McSNAC may be limited to approximating indirect interactions between protein species, as cytometry experiments are only able to assay a small fraction of protein species involved in signaling. Results: We carry out a series of in silico experiments here to show (1) McSNAC is capable of accurately estimating the ground-truth model in a scalable manner when given data originating from a first-order system; (2) McSNAC is capable of qualitatively predicting outcomes to perturbations of species abundances in simple second-order reaction models and in a complex in silico nonlinear signaling network in which some proteins are unmeasured. Conclusions: These findings demonstrate that McSNAC can be a valuable screening tool for generating models of signaling networks from time-stamped CyTOF data.

BioNetGMMFit: estimating parameters of a BioNetGen model from time-stamped snapshots of single cells.

Mechanistic models are commonly employed to describe signaling and gene regulatory kinetics in single cells and cell populations. Recent advances in single-cell technologies have produced multidimensional datasets where snapshots of copy numbers (or abundances) of a large number of proteins and mRNA are measured across time in single cells. The availability of such datasets presents an attractive scenario where mechanistic models are validated against experiments, and estimated model parameters enable quantitative predictions of signaling or gene regulatory kinetics. To empower the systems biology community to easily estimate parameters accurately from multidimensional single-cell data, we have merged a widely used rule-based modeling software package BioNetGen, which provides a user-friendly way to code for mechanistic models describing biochemical reactions, and the recently introduced CyGMM, that uses cell-to-cell differences to improve parameter estimation for such networks, into a single software package: BioNetGMMFit. BioNetGMMFit provides parameter estimates of the model, supplied by the user in the BioNetGen markup language (BNGL), which yield the best fit for the observed single-cell, time-stamped data of cellular components. Furthermore, for more precise estimates, our software generates confidence intervals around each model parameter. BioNetGMMFit is capable of fitting datasets of increasing cell population sizes for any mechanistic model specified in the BioNetGen markup language. By streamlining the process of developing mechanistic models for large single-cell datasets, BioNetGMMFit provides an easily-accessible modeling framework designed for scale and the broader biochemical signaling community.

Decreased diacylglycerol metabolism enhances ERK activation and augments CD8+ T cell functional responses.

Modulation of T cell receptor signal transduction in CD8(+) T cells represents a novel strategy toward enhancing the immune response to tumor. Recently, levels of guanine exchange factors, RasGRP and SOS, within T cells have been shown to represent a key determinant in the regulation of the analog to the digital activation threshold of Ras. One important for regulating activation levels of RasGRP is diacylglycerol (DAG), and its levels are influenced by diacylglycerol kinase-ζ (DGKζ), which metabolizes DAG into phosphatidic acid, terminating DAG-mediated Ras signaling. We sought to determine whether DGKζ-deficient CD8(+) T cells demonstrated enhanced in vitro responses in a manner predicted by the current model of Ras activation and to evaluate whether targeting this threshold confers enhanced CD8(+) T cell responsiveness to tumor. We observed that DGKζ-deficient CD8(+) T cells conform to most predictions of the current model of how RasGRP levels influence Ras activation. But our results differ in that the EC(50) value of stimulation is not altered for any T cell receptor stimulus, a finding that suggests a further degree of complexity to how DGKζ deficiency affects signals important for Ras and ERK activation. Additionally, we found that DGKζ-deficient CD8(+) T cells demonstrate enhanced responsiveness in a subcutaneous lymphoma model, implicating the analog to a digital conversion threshold as a novel target for potential therapeutic manipulation.

Origin of the sharp boundary that discriminates positive and negative selection of thymocytes.

T lymphocytes play a key role in adaptive immunity and are activated by interactions of their T cell receptors (TCR) with peptides (p) derived from antigenic proteins bound to MHC gene products. The repertoire of T lymphocytes available in peripheral organs is tuned in the thymus. Immature T lymphocytes (thymocytes) interact with diverse endogenous peptides bound to MHC in the thymus. TCR expressed on thymocytes must bind weakly to endogenous pMHC (positive selection) but must not bind too strongly to them (negative selection) to emerge from the thymus. Negatively selecting pMHC ligands bind TCR with a binding affinity that exceeds a sharply defined (digital) threshold. In contrast, there is no sharp threshold separating positively selecting ligands from those that bind too weakly to elicit a response. We describe results of computer simulations and experiments, which suggest that the contrast between the characters of the positive and negative selection thresholds originates in differences in the way in which Ras proteins are activated by ligands of varying potency. The molecular mechanism suggested by our studies generates hypotheses for how genetic aberrations may dampen the digital negative selection response, with concomitant escape of autoimmune T lymphocytes from the thymus.