Sayak Mukherjee

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

Significance The relationship between form and function is ubiquitous in biology. Using a method (maximum entropy) from statistical physics, we investigated how function regulates form in the context of Escherichia coli chemotaxis. We found that the nearly perfect and robust chemotaxis behavior (function) does not fully determine the cell-to-cell variations of chemotaxis protein abundances (form) in E. coli. We show that additional constraints imposed by the protein synthesis machinery and nonchemotactic cell functions in conjunction with the constraints imposed by the chemotaxis program are required to determine the observed variations of protein abundances. This demonstrates that properties of a modular component (e.g., the chemotaxis signaling module) in a biological network also depend on the system of which the module is a part. 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.

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.

Dramatic reduction of dimensionality in large biochemical networks owing to strong pair correlations

Large multi-dimensionality of high-throughput datasets pertaining to cell signalling and gene regulation renders it difficult to extract mechanisms underlying the complex kinetics involving various biochemical compounds (e.g. proteins and lipids). Data-driven models often circumvent this difficulty by using pair correlations of the protein expression levels to produce a small number (fewer than 10) of principal components, each a linear combination of the concentrations, to successfully model how cells respond to different stimuli. However, it is not understood if this reduction is specific to a particular biological system or to nature of the stimuli used in these experiments. We study temporal changes in pair correlations, described by the covariance matrix, between concentrations of different molecular species that evolve following deterministic mass-action kinetics in large biologically relevant reaction networks and show that this dramatic reduction of dimensions (from hundreds to less than five) arises from the strong correlations between different species at any time and is insensitive to the form of the nonlinear interactions, network architecture, and to a wide range of values of rate constants and concentrations. We relate temporal changes in the eigenvalue spectrum of the covariance matrix to low-dimensional, local changes in directions of the system trajectory embedded in much larger dimensions using elementary differential geometry. We illustrate how to extract biologically relevant insights such as identifying significant timescales and groups of correlated chemical species from our analysis. Our work provides for the first time, to our knowledge, a theoretical underpinning for the successful experimental analysis and points to a way to extract mechanisms from large-scale high-throughput datasets.

In silico modeling identifies CD45 as a regulator of IL-2 synergy in the NKG2D-mediated activation of immature human NK cells

The basis for how the cytokine IL-2 boosts the activation of natural killer cells in response to NKG2D stimulation is uncovered. Searching for synergy Natural killer (NK) cells detect and kill virally infected and transformed cells. NK cell activation depends on the balance between signaling by inhibitory and activating receptors, and cytokine signaling can synergize with activating receptor signaling to induce NK cell activation. Mukherjee et al. performed mass cytometry analysis of the abundances of more than 30 proteins and computational analysis of the relationships between those changes in abundance. The authors delineated the mechanism underlying the synergy between signaling by the cytokine interleukin-2 (IL-2) and subsequent stimulation of the activating receptor NKG2D in immature and mature subsets of human NK cells. This analysis predicted and experiments verified that the IL-2–stimulated increase in the abundance of the phosphatase CD45 in immature NK cells was the major determinant of the enhanced responses of these cells to NKG2D stimulation. The application of this type of analysis to other immune cell types will help to discover other synergies underlying cellular activation and function. Natural killer (NK) cells perform immunosurveillance of virally infected and transformed cells, and their activation depends on the balance between signaling by inhibitory and activating receptors. Cytokine receptor signaling can synergize with activating receptor signaling to induce NK cell activation. We investigated the interplay between the signaling pathways stimulated by the cytokine interleukin-2 (IL-2) and the activating receptor NKG2D in immature (CD56bright) and mature (CD56dim) subsets of human primary NK cells using mass cytometry experiments and in silico modeling. Our analysis revealed that IL-2 changed the abundances of several key proteins, including NKG2D and the phosphatase CD45. Furthermore, we found differences in correlations between protein abundances, which were associated with the maturation state of the NK cells. The mass cytometry measurements also revealed that the signaling kinetics of key protein abundances induced by NKG2D stimulation depended on the maturation state and the pretreatment condition of the NK cells. Our in silico model, which described the multidimensional data with coupled first-order reactions, predicted that the increase in CD45 abundance was a major enhancer of NKG2D-mediated activation in IL-2–treated CD56bright NK cells but not in IL-2–treated CD56dim NK cells. This dependence on CD45 was verified by measurement of CD107a mobilization to the NK cell surface (a marker of activation). Our mathematical framework can be used to glean mechanisms underlying synergistic signaling pathways in other activated immune cells.

Non-canonical antagonism of PI3K by the kinase Itpkb delays thymocyte β-selection and renders it Notch-dependent

β-selection is the most pivotal event determining αβ T cell fate. Here, surface-expression of a pre-T cell receptor (pre-TCR) induces thymocyte metabolic activation, proliferation, survival and differentiation. Besides the pre-TCR, β-selection also requires co-stimulatory signals from Notch receptors - key cell fate determinants in eukaryotes. Here, we show that this Notch-dependence is established through antagonistic signaling by the pre-TCR/Notch effector, phosphoinositide 3-kinase (PI3K), and by inositol-trisphosphate 3-kinase B (Itpkb). Canonically, PI3K is counteracted by the lipid-phosphatases Pten and Inpp5d/SHIP-1. In contrast, Itpkb dampens pre-TCR induced PI3K/Akt signaling by producing IP4, a soluble antagonist of the Akt-activating PI3K-product PIP3. Itpkb-/- thymocytes are pre-TCR hyperresponsive, hyperactivate Akt, downstream mTOR and metabolism, undergo an accelerated β-selection and can develop to CD4+CD8+ cells without Notch. This is reversed by inhibition of Akt, mTOR or glucose metabolism. Thus, non-canonical PI3K-antagonism by Itpkb restricts pre-TCR induced metabolic activation to enforce coincidence-detection of pre-TCR expression and Notch-engagement. DOI: http://dx.doi.org/10.7554/eLife.10786.001

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.

In Silico Modeling of Itk Activation Kinetics in Thymocytes Suggests Competing Positive and Negative IP4 Mediated Feedbacks Increase Robustness

The inositol-phosphate messenger inositol(1,3,4,5)tetrakisphosphate (IP4) is essential for thymocyte positive selection by regulating plasma-membrane association of the protein tyrosine kinase Itk downstream of the T cell receptor (TCR). IP4 can act as a soluble analog of the phosphoinositide 3-kinase (PI3K) membrane lipid product phosphatidylinositol(3,4,5)trisphosphate (PIP3). PIP3 recruits signaling proteins such as Itk to cellular membranes by binding to PH and other domains. In thymocytes, low-dose IP4 binding to the Itk PH domain surprisingly promoted and high-dose IP4 inhibited PIP3 binding of Itk PH domains. However, the mechanisms that underlie the regulation of membrane recruitment of Itk by IP4 and PIP3 remain unclear. The distinct Itk PH domain ability to oligomerize is consistent with a cooperative-allosteric mode of IP4 action. However, other possibilities cannot be ruled out due to difficulties in quantitatively measuring the interactions between Itk, IP4 and PIP3, and in generating non-oligomerizing Itk PH domain mutants. This has hindered a full mechanistic understanding of how IP4 controls Itk function. By combining experimentally measured kinetics of PLCγ1 phosphorylation by Itk with in silico modeling of multiple Itk signaling circuits and a maximum entropy (MaxEnt) based computational approach, we show that those in silico models which are most robust against variations of protein and lipid expression levels and kinetic rates at the single cell level share a cooperative-allosteric mode of Itk regulation by IP4 involving oligomeric Itk PH domains at the plasma membrane. This identifies MaxEnt as an excellent tool for quantifying robustness for complex TCR signaling circuits and provides testable predictions to further elucidate a controversial mechanism of PIP3 signaling.

Connecting the dots across time: reconstruction of single-cell signalling trajectories using time-stamped data

Single-cell responses are shaped by the geometry of signalling kinetic trajectories carved in a multidimensional space spanned by signalling protein abundances. It is, however, challenging to assay a large number (more than 3) of signalling species in live-cell imaging, which makes it difficult to probe single-cell signalling kinetic trajectories in large dimensions. Flow and mass cytometry techniques can measure a large number (4 to more than 40) of signalling species but are unable to track single cells. Thus, cytometry experiments provide detailed time-stamped snapshots of single-cell signalling kinetics. Is it possible to use the time-stamped cytometry data to reconstruct single-cell signalling trajectories? Borrowing concepts of conserved and slow variables from non-equilibrium statistical physics we develop an approach to reconstruct signalling trajectories using snapshot data by creating new variables that remain invariant or vary slowly during the signalling kinetics. We apply this approach to reconstruct trajectories using snapshot data obtained from in silico simulations, live-cell imaging measurements, and, synthetic flow cytometry datasets. The application of invariants and slow variables to reconstruct trajectories provides a radically different way to track objects using snapshot data. The approach is likely to have implications for solving matching problems in a wide range of disciplines.

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.