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.

Stochastic modeling of influenza spread dynamics with recurrences.

We present results of a study of a simple, stochastic, agent-based model of influenza A infection, simulating its dynamics over the course of one flu season. Building on an early work of Bartlett, we define a model with a limited number of parameters and rates that have clear epidemiological interpretation and can be constrained by data. We demonstrate the occurrence of recurrent behavior in the infected number [more than one peak in a season], which is observed in data, in our simulations for populations consisting of cohorts with strong intra- and weak inter-cohort transmissibility. We examine the dependence of the results on epidemiological and population characteristics by investigating their dependence on a range of parameter values. Finally, we study infection with two strains of influenza, inspired by observations, and show a counter-intuitive result for the effect of inoculation against the strain that leads to the first wave of infection.

Spatio-temporal dynamics of Host-Virus competition: A model study of influenza A.

We present results of a study of the early-time response of the innate immune system to influenza virus infection in an agent-based model (ABM) of epithelial cell layers. We find that the competition between the anti-viral immune response and viral antagonism can lead to viral titers non-monotonic in the initial infection fraction as found in experiments. Our model includes a coarse-grained version of intra-cellular processes and inter-cellular communication via cytokine and virion diffusion. We use ABM to follow the propagation of viral infection in the layer and the increase of the viral load as a function of time for different values of the multiplicity of infection (MOI), the initial number of viruses added per cell. We find that for moderately strong host immune response, the number of infected cells and viral load for a smaller MOI exceeds that for larger MOI, as seen in experiments. We elucidate the mechanism underlying this result as the synergistic action of cytokines secreted by infected cells in controlling viral amplification for larger MOI. We investigate the length and time scales that determine this non-monotonic behavior within the ABM. We study the diffusive spread of virions and cytokines from a single infected cell in an absorbing medium analytically and numerically and deduce the length scale that yields a good estimate of the MOI at which we find non-monotonicity. Detailed computations of the temporal behavior of averaged quantities and spatial measures provide further insights into host-viral interactions and connections to experimental observations.

Stochastic Sequestration Promotes Specificity in Decision Making in Single Cells.

Cellular functions are mediated by specific molecular interactions; however, often competing nonspecific interactions can occur instead, for example, in noncoding regions of genes during transcription or in the response of cell receptors to external signals. Various functional roles have been proposed for such interactions. Motivated by these considerations, we study the time-dependent behavior of a class of discrete, stochastic models in which decoy molecules mediate nonspecific reactions that sequester activated molecules. It is shown that such nonspecific interactions can lead to a time delay in the completion of the specific reaction by the activated molecule, thus permitting discrimination between signals of different duration. We study the effect of stochastic fluctuations in a simple model of gene transcription by numerical solution of the Master Equation and find that the distribution of first passage times for the specific reaction shows surprising nonexponential (non-Debye) behavior over a range of time scales. The mathematical mechanism underlying this behavior is explained in terms of the behavior of the eigensystem of the linear operator associated with the time evolution. Our results demonstrate that stochastic sequestration can be used to enhance the specificity achieved by the well-known kinetic proofreading mechanism.

Innate Immune Response to Influenza Virus at Single-Cell Resolution in Human Epithelial Cells Revealed Paracrine Induction of Interferon Lambda 1.

Early interactions of influenza A virus (IAV) with respiratory epithelium might determine the outcome of infection. The study of global cellular innate immune responses often masks multiple aspects of the mechanisms by which populations of cells work as organized and heterogeneous systems to defeat virus infection, and how the virus counteracts these systems. In this study, we experimentally dissected the dynamics of IAV and human epithelial respiratory cell interaction during early infection at the single-cell level. We found that the number of viruses infecting a cell (multiplicity of infection [MOI]) influences the magnitude of virus antagonism of the host innate antiviral response. Infections performed at high MOIs resulted in increased viral gene expression per cell and stronger antagonist effect than infections at low MOIs. In addition, single-cell patterns of expression of interferons (IFN) and IFN-stimulated genes (ISGs) provided important insights into the contributions of the infected and bystander cells to the innate immune responses during infection. Specifically, the expression of multiple ISGs was lower in infected than in bystander cells. In contrast with other IFNs, IFN lambda 1 (IFNL1) showed a widespread pattern of expression, suggesting a different cell-to-cell propagation mechanism more reliant on paracrine signaling. Finally, we measured the dynamics of the antiviral response in primary human epithelial cells, which highlighted the importance of early innate immune responses at inhibiting virus spread.IMPORTANCE Influenza A virus (IAV) is a respiratory pathogen of high importance to public health. Annual epidemics of seasonal IAV infections in humans are a significant public health and economic burden. IAV also causes sporadic pandemics, which can have devastating effects. The main target cells for IAV replication are epithelial cells in the respiratory epithelium. The cellular innate immune responses induced in these cells upon infection are critical for defense against the virus, and therefore, it is important to understand the complex interactions between the virus and the host cells. In this study, we investigated the innate immune response to IAV in the respiratory epithelium at the single-cell level, providing a better understanding on how a population of epithelial cells functions as a complex system to orchestrate the response to virus infection and how the virus counteracts this system.

Rising Variability, Not Slowing Down, as a Leading Indicator of a Stochastically Driven Abrupt Transition in a Dryland Ecosystem.

Complex systems can undergo abrupt state transitions near critical points. Theory and controlled experimental studies suggest that the approach to critical points can be anticipated by critical slowing down (CSD), that is, a characteristic slowdown in the dynamics. The validity of this indicator in field ecosystems, where stochasticity is important in driving transitions, remains unclear. We analyze long-term data from a dryland ecosystem in the Shapotou region of China and show that the ecosystem underwent an abrupt transition from a nearly bare to a moderate grass cover state. Prior to the transition, the system showed no (or weak) signatures of CSD but exhibited expected increasing trends in the variability of the grass cover, quantified by variance and skewness. These surprising results are consistent with the theoretical expectation of stochastically driven abrupt transitions that occur away from critical points; indeed, a driver of vegetation-annual rainfall-showed rising variance prior to the transition. Our study suggests that rising variability can potentially serve as a leading indicator of stochastically driven transitions in real-world ecosystems.

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 effect of spin transport on spin lifetime in nanoscale systems.

Spintronics use the electron spin as a state variable for information processing and storage. This requires manipulation of spin ensembles for data encoding, and spin transport for information transfer. Because of the central importance of lifetime for understanding and controlling spins, mechanisms that determine this lifetime in bulk systems have been extensively studied. However, a clear understanding of few-spin systems remains challenging. Here, we report spatially resolved magnetic resonance studies of electron spin ensembles confined to a 'spin nanowire' formed by nitrogen ion implantation in diamond. We measure the spin lifetime of the ensemble--that is, its spin autocorrelation time--by monitoring the statistical fluctuations of its net moment, which is in thermal equilibrium and has no imposed polarization gradient. We find that the lifetime of the ensemble is dominated by spin transport from the ensemble into the adjacent spin reservoir that is provided by the remainder of the nanowire. This is in striking contrast to conventional spin-lattice relaxation measurements of isolated spin ensembles. Electron spin resonance spectroscopy performed on nanoscale spin ensembles by means of a novel spin manipulation protocol corroborates spin transport in strong field gradients. Our experiments, supported by microscopic Monte Carlo modelling, provide a unique insight into the intrinsic dynamics of pure spin currents needed for nanoscale devices that seek to control spins.

Noise propagation through extracellular signaling leads to fluctuations in gene expression.

BACKGROUND: Cell-to-cell variability in mRNA and proteins has been observed in many biological systems, including the human innate immune response to viral infection. Most of these studies have focused on variability that arises from (a) intrinsic stochastic fluctuations in gene expression and (b) extrinsic sources (e.g. fluctuations in transcription factors). The main focus of our study is the effect of extracellular signaling on enhancing intrinsic stochastic fluctuations. As a new source of noise, the communication between cells with fluctuating numbers of components has received little attention. We use agent-based modeling to study this contribution to noise in a system of human dendritic cells responding to viral infection. RESULTS: Our results, validated by single-cell experiments, show that in the transient state cell-to-cell variability in an interferon-stimulated gene (DDX58) arises from the interplay between the spatial randomness of the cellular sources of the interferon and the temporal stochasticity of its own production. The numerical simulations give insight into the time scales on which autocrine and paracrine signaling act in a heterogeneous population of dendritic cells upon viral infection. We study the effect of different factors that influence the magnitude of the cell-to-cell-variability of the induced gene, including the cell density, multiplicity of infection, and the time scale over which the cellular sources begin producing the cytokine. CONCLUSIONS: We propose a mechanism of noise propagation through extracellular communication and establish conditions under which the mechanism is operative. The cellular stochasticity of gene induction, which we investigate, is not limited to the specific interferon-induced gene we have studied; a broad distribution of copy numbers across cells is to be expected for other interferon-stimulated genes. This can lead to functional consequences for the system-level response to a viral challenge.

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.

Changing skewness: an early warning signal of regime shifts in ecosystems.

Empirical evidence for large-scale abrupt changes in ecosystems such as lakes and vegetation of semi-arid regions is growing. Such changes, called regime shifts, can lead to degradation of ecological services. We study simple ecological models that show a catastrophic transition as a control parameter is varied and propose a novel early warning signal that exploits two ubiquitous features of ecological systems: nonlinearity and large external fluctuations. Either reduced resilience or increased external fluctuations can tip ecosystems to an alternative stable state. It is shown that changes in asymmetry in the distribution of time series data, quantified by changing skewness, is a model-independent and reliable early warning signal for both routes to regime shifts. Furthermore, using model simulations that mimic field measurements and a simple analysis of real data from abrupt climate change in the Sahara, we study the feasibility of skewness calculations using data available from routine monitoring.

Chromosome-specific and noisy IFNB1 transcription in individual virus-infected human primary dendritic cells.

The induction of interferon beta (IFNB1) is a key event in the antiviral immune response. We studied the role of transcriptional noise in the regulation of the IFNB1 locus in primary cultures of human dendritic cells (DCs), which are important 'first responders' to viral infection. In single cell assays, IFNB1 mRNA expression in virus-infected DCs showed much greater cell-to-cell variation than that of a housekeeping gene, another induced transcript and viral RNA. We determined the contribution of intrinsic noise by measuring the allelic origin of transcripts in each cell and found that intrinsic noise is a very significant part of total noise. We developed a stochastic model to investigate the underlying mechanisms. We propose that the surprisingly high levels of IFNB1 transcript noise originate from the complexity of IFNB1 enhanceosome formation, which leads to a range up to many minutes in the differences within each cell in the time of activation of each allele.