Noise decomposition of intracellular biochemical signaling networks using nonequivalent reporters

Modulating the dynamics of NFκB and PI3K enhances the ensemble-level TNFR1 signaling mediated apoptotic response

Cell-to-cell variability during TNFα stimulated Tumor Necrosis Factor Receptor 1 (TNFR1) signaling can lead to single-cell level pro-survival and apoptotic responses. This variability stems from the heterogeneity in signal flow through intracellular signaling entities that regulate the balance between these two phenotypes. Using systematic Boolean dynamic modeling of a TNFR1 signaling network, we demonstrate that the signal flow path variability can be modulated to enable cells favour apoptosis. We developed a computationally efficient approach "Boolean Modeling based Prediction of Steady-state probability of Phenotype Reachability (BM-ProSPR)" to accurately predict the network's ability to settle into different phenotypes. Model analysis juxtaposed with the experimental observations revealed that NFκB and PI3K transient responses guide the XIAP behaviour to coordinate the crucial dynamic cross-talk between the pro-survival and apoptotic arms at the single-cell level. Model predicted the experimental observations that ~31% apoptosis increase can be achieved by arresting Comp1 - IKK* activity which regulates the NFκB and PI3K dynamics. Arresting Comp1 - IKK* activity causes signal flow path re-wiring towards apoptosis without significantly compromising NFκB levels, which govern adequate cell survival. Priming an ensemble of cancerous cells with inhibitors targeting the specific interaction involving Comp1 and IKK* prior to TNFα exposure could enable driving them towards apoptosis.

Understanding the physical mechanism of intrinsic noise inside viscous isotropic solids

We report acoustic impulse-response and system function of particle vibration inside viscous, dense solids and explain the physical mechanism of intrinsic-noise generation. With an external disturbance of a harmonic force acting on particles inside viscous solid media, the system of particle vibration goes through a gradual transition from a static state to a steady harmonic vibrational state. Based on the damped oscillator model, the transition frequency spectrum resembles the intrinsic noise generated by vibrating particles in viscous isotropic solids, which delivers a crucial understanding for applications to invert stratum characteristics around the drilled oil well and its abnormal geological structure.

Quantifying information of intracellular signaling: progress with machine learning

Cells convey information about their extracellular environment to their core functional machineries. Studying the capacity of intracellular signaling pathways to transmit information addresses fundamental questions about living systems. Here, we review how information-theoretic approaches have been used to quantify information transmission by signaling pathways that are functionally pleiotropic and subject to molecular stochasticity. We describe how recent advances in machine learning have been leveraged to address the challenges of complex temporal trajectory datasets and how these have contributed to our understanding of how cells employ temporal coding to appropriately adapt to environmental perturbations.

Pathway-resolved decomposition demonstrates correlation and noise dependencies of redundant information processing in recurrent feed-forward topologies

In a biochemical assay that converts fan-in networks into feed-forward loops (FFLs), we show that the inter-regulator redundant information about the output gene product can be decomposed into finer components, mediated by the constituent pathways. Variance-based information within the linear noise regime facilitates quantifying these submodular redundancies. Contrary to the conventional wisdom on information decomposition, we report that information redundancy depends nontrivially on inter-regulator correlation. For the type-1 coherent (C1) and incoherent (I1) FFLs, the direct regulatory path-mediated redundancy is certainly correlation independent. However, components induced by the indirect regulatory path and interpathway interference are correlation dependent in (non)linear fashion. The trade-off between information redundancy and similarly decomposable extrinsic noise from input to output node has been demonstrated for the pathways and full motifs. Our analyses suggest that the interpathway cross redundancy positively and negatively influences the superposition of elementary redundancies in the C1- and I1-FFLs, respectively. Their corresponding total extrinsic noise is produced by the weighted sum and difference of the pathway-specific components. We find that the I1-FFL is able to manufacture more varied redundancy and extrinsic noise responses compared to the C1-FFL. Underlying the differing characteristics of the composite metrics across FFL variants, there exist uniformly behaving pathway-dependent elements. The decomposition framework has been meticulously explored in biologically rational parametric realizations through analytical estimates and stochastic simulations.

Inferring gene regulation dynamics from static snapshots of gene expression variability

Inferring functional relationships within complex networks from static snapshots of a subset of variables is a ubiquitous problem in science. For example, a key challenge of systems biology is to translate cellular heterogeneity data obtained from single-cell sequencing or flow-cytometry experiments into regulatory dynamics. We show how static population snapshots of covariability can be exploited to rigorously infer properties of gene expression dynamics when gene expression reporters probe their upstream dynamics on separate timescales. This can be experimentally exploited in dual-reporter experiments with fluorescent proteins of unequal maturation times, thus turning an experimental bug into an analysis feature. We derive correlation conditions that detect the presence of closed-loop feedback regulation in gene regulatory networks. Furthermore, we show how genes with cell-cycle-dependent transcription rates can be identified from the variability of coregulated fluorescent proteins. Similar correlation constraints might prove useful in other areas of science in which static correlation snapshots are used to infer causal connections between dynamically interacting components.

Concepts and Applications of Information Theory to Immuno-Oncology

Recent successes of immune-modulating therapies for cancer have stimulated research on information flow within the immune system and, in turn, clinical applications of concepts from information theory. Through information theory, one can describe and formalize, in a mathematically rigorous fashion, the function of interconnected components of the immune system in health and disease. Specifically, using concepts including entropy, mutual information, and channel capacity, one can quantify the storage, transmission, encoding, and flow of information within and between cellular components of the immune system on multiple temporal and spatial scales. To understand, at the quantitative level, immune signaling function and dysfunction in cancer, we present a methodology-oriented review of information-theoretic treatment of biochemical signal transduction and transmission coupled with mathematical modeling.

Role of integrated noise in pathway-specific signal propagation in feed-forward loops

Cells impose optimal noise control mechanism in diverse situations to cope with distinct environmental cues. Sometimes, it is desirable for the cell to utilize fluctuations for noise-driven processes. In other cases, noise can be harmful to the cell to show optimal fitness. It is, therefore, important to unravel the noise propagation mechanism inside the cell. Such noise controlling mechanism is accomplished by using gene transcription regulatory networks. One such gene regulatory network is feed-forward loop, having three regulatory nodes S, X and Y. Here, we consider the most abundant type 1 of coherent and incoherent feed-forward loops with both OR and AND logic functions, forming four different architectures. In OR logic function, the functions representing S and X act additively for the regulation of Y, while in AND logic function, the same functions (S and X) act multiplicatively for the regulation of Y. Measurement of susceptibility of the signal at output Y is done using elasticity of each regulation in FFLs. Using susceptibility, we demonstrate the nature of pathway integration by which one-step and two-step pathways get overlapped. The integration type is competitive for motifs having OR gate, while it is noncompetitive for the same with AND gate. The pathway integration property explains the output noise behavior of the motifs properly but cannot infer about the mechanism by which the upstream noise propagates to output. To account this, the total output noise is decomposed, which results in integrated noise as an additional noise source along with pathway-specific noise components. The integrated noise is found to appear as a consequence of integration between the pathways and has different functional characteristics explaining noise amplification and noise attenuation property of coherent and incoherent feed-forward loops, respectively. The noise decomposition also quantifies the contribution of different noise sources toward total noise. Finally, the noise propagation is being tuned as a function of input signal noise and its time scale of fluctuations, which shows considerable intrinsic noise strength and relatively slow relaxation time scale causes a higher degree of noise propagation in FFLs.

Sensitivity minimization, biological homeostasis and information theory

All organisms must be able to adapt to changes in the environment. To this end, they have developed sophisticated regulatory mechanisms to ensure homeostasis. Control engineers, who must design similar regulatory systems, have developed a number of general principles that govern feedback regulation. These lead to constraints which impose trade-offs that arise when developing controllers to minimize the effect of external disturbances on systems. Here, we review some of these trade-offs, particularly Bode's integral formula. We also highlight its connection to information theory, by showing that the constraints in sensitivity minimization can be cast as limitations on the information transmission through a system, and these have their root in causality. Finally, we look at how these constraints arise in two biological systems: glycolytic oscillations and the energy cost of perfect adaptation in a bacterial chemotactic pathway.

The common misuse of noise decomposition as applied to genetic systems

The noise-decomposition technique is applied in several fields, including genetic systems, optical images, recording, and navigation. In genetic systems, noise decomposition is usually achieved by using two reporters [Elowitz M.B., Levine A.J., Siggia E.D., Swain P·S., 2002. Stochastic gene expression in a single cell. Science 297, 1183-6.]. A reporter is a protein with fluorescence, an RNA hybridized with a fluorescent probe, or any other detectable intracellular component. If a reporter is constructed in addition to the original reporter, the system's stochasticity may change. Such phenomena became severe for genes in plasmids with a high copy number. By SSA (stochastic simulation algorithm), we observed an approximately 50% increment in the coefficient of variation while introducing additional reporters. Besides, if two reporters respond to the upstream element at a different time, the trunk noise (or extrinsic noise) cannot be accurately determined. This is because the "calculative trunk noise" changes along with the delay, though the real trunk noise does not. For RNA reporters, a 5-min transcriptional delay caused a calculative trunk noise that was 90% less than the real trunk noise. Fortunately, this problem is negligible when the degradation rate constant is low, and it is usually true in the case of the protein reporters. One can check the lifespan of the reporter before applying the noise-decomposition technique.

Gene-Specific Linear Trends Constrain Transcriptional Variability of the Toll-like Receptor Signaling

Single-cell gene expression is inherently variable, but how this variability is controlled in response to stimulation remains unclear. Here, we use single-cell RNA-seq and single-molecule mRNA counting (smFISH) to study inducible gene expression in the immune toll-like receptor system. We show that mRNA counts of tumor necrosis factor α conform to a standard stochastic switch model, while transcription of interleukin-1β involves an additional regulatory step resulting in increased heterogeneity. Despite different modes of regulation, systematic analysis of single-cell data for a range of genes demonstrates that the variability in transcript count is linearly constrained by the mean response over a range of conditions. Mathematical modeling of smFISH counts and experimental perturbation of chromatin state demonstrates that linear constraints emerge through modulation of transcriptional bursting along with gene-specific relationships. Overall, our analyses demonstrate that the variability of the inducible single-cell mRNA response is constrained by transcriptional bursting.

•

Single-cell TNF-α and IL-1β mRNA responses are differentially controlled

•

Variability of TLR-induced responses scale linearly with mean mRNA counts

•

Gene-specific constraints emerge via modulation of transcriptional bursting

•

Chromatin state regulates transcriptional bursting of IL-1β

Allele-specific single-cell RNA sequencing reveals different architectures of intrinsic and extrinsic gene expression noises

Gene expression noise refers to the variation of the expression level of a gene among isogenic cells in the same environment, and has two sources: extrinsic noise arising from the disparity of the cell state and intrinsic noise arising from the stochastic process of gene expression in the same cell state. Due to the low throughput of the existing method for measuring the two noise components, the architectures of intrinsic and extrinsic expression noises remain elusive. Using allele-specific single-cell RNA sequencing, we here estimate the two noise components of 3975 genes in mouse fibroblast cells. Our analyses verify predicted influences of several factors such as the TATA-box and microRNA targeting on intrinsic or extrinsic noises and reveal gene function-associated noise trends implicating the action of natural selection. These findings unravel differential regulations, optimizations, and biological consequences of intrinsic and extrinsic noises and can aid the construction of desired synthetic circuits.

Insights about collective decision-making at the genetic level

By living in a collective, individuals can share and aggregate information to base their decisions on the many rather than on the one, thereby increasing accuracy. But a collective can also be defined at the molecular level. In the following, we reason that genes, by working collectively, share fundamental features with social organisms, which ends, without invoking cognition, in wiser responses. For that, we compile into a single picture the terms redundancy, stochastic resonance, intrinsic and extrinsic noise, and cross-regulation.

Noise in the Vertebrate Segmentation Clock Is Boosted by Time Delays but Tamed by Notch Signaling

Taming cell-to-cell variability in gene expression is critical for precise pattern formation during embryonic development. To investigate the source and buffering mechanism of expression variability, we studied a biological clock, the vertebrate segmentation clock, controlling the precise spatiotemporal patterning of the vertebral column. By counting single transcripts of segmentation clock genes in zebrafish, we show that clock genes have low RNA amplitudes and expression variability is primarily driven by gene extrinsic sources, which is suppressed by Notch signaling. We further show that expression noise surprisingly increases from the posterior progenitor zone to the anterior segmentation and differentiation zone. Our computational model reproduces the spatial noise profile by incorporating spatially increasing time delays in gene expression. Our results, suggesting that expression variability is controlled by the balance of time delays and cell signaling in a vertebrate tissue, will shed light on the accuracy of natural clocks in multi-cellular systems and inspire engineering of robust synthetic oscillators.

On Information Extraction and Decoding Mechanisms Improved by Noisy Amplification in Signaling Pathways

The cells need to process information about extracellular stimuli. They encode, transmit and decode the information to elicit an appropriate response. Studies aimed at understanding how such information is decoded in the signaling pathways to generate a specific cellular response have become essential. Eukaryotic cells decode information through two different mechanisms: the feed-forward loop and the promoter affinity. Here, we investigate how these two mechanisms improve information transmission. A detailed comparison is made between the stochastic model of the MAPK/ERK pathway and a stochastic minimal decoding model. The maximal amount of transmittable information was computed. The results suggest that the decoding mechanism of the MAPK/ERK pathway improve the channel capacity because it behaves as a noisy amplifier. We show a positive dependence between the noisy amplification and the amount of information extracted. Additionally, we show that the extrinsic noise can be tuned to improve information transmission. This investigation has revealed that the feed-forward loop and the promoter affinity motifs extract information thanks to processes of amplification and noise addition. Moreover, the channel capacity is enhanced when both decoding mechanisms are coupled. Altogether, these findings suggest novel characteristics in how decoding mechanisms improve information transmission.

Interplay of synergy and redundancy in diamond motif

The formalism of partial information decomposition provides a number of independent components which altogether constitute the total information provided by the source variable(s) about the target variable(s). These non-overlapping terms are recognized as unique information, synergistic information, and redundant information. The metric of net synergy conceived as the difference between synergistic and redundant information is capable of detecting effective synergy, effective redundancy, and information independence among stochastic variables. The net synergy can be quantified using appropriate combinations of different Shannon mutual information terms. The utilization of the net synergy in network motifs with the nodes representing different biochemical species, involved in information sharing, uncovers rich store for exciting results. In the current study, we use this formalism to obtain a comprehensive understanding of the relative information processing mechanism in a diamond motif and two of its sub-motifs, namely, bifurcation and integration motif embedded within the diamond motif. The emerging patterns of effective synergy and effective redundancy and their contribution toward ensuring high fidelity information transmission are duly compared in the sub-motifs. Investigation on the metric of net synergy in independent bifurcation and integration motifs are also executed. In all of these computations, the crucial roles played by various systemic time scales, activation coefficients, and signal integration mechanisms at the output of the network topologies are especially emphasized. Following this plan of action, we become confident that the origin of effective synergy and effective redundancy can be architecturally justified by decomposing a diamond motif into bifurcation and integration motif. According to our conjecture, the presence of a common source of fluctuations creates effective redundancy. Our calculations reveal that effective redundancy empowers signal fidelity. Moreover, to achieve this, input signaling species avoids strong interaction with downstream intermediates. This strategy is capable of making the diamond motif noise-tolerant. Apart from the topological features, our study also puts forward the active contribution of additive and multiplicative signal integration mechanisms to nurture effective redundancy and effective synergy.

Cell-specific responses to the cytokine TGFβ are determined by variability in protein levels

The cytokine TGFβ provides important information during embryonic development, adult tissue homeostasis, and regeneration. Alterations in the cellular response to TGFβ are involved in severe human diseases. To understand how cells encode the extracellular input and transmit its information to elicit appropriate responses, we acquired quantitative time-resolved measurements of pathway activation at the single-cell level. We established dynamic time warping to quantitatively compare signaling dynamics of thousands of individual cells and described heterogeneous single-cell responses by mathematical modeling. Our combined experimental and theoretical study revealed that the response to a given dose of TGFβ is determined cell specifically by the levels of defined signaling proteins. This heterogeneity in signaling protein expression leads to decomposition of cells into classes with qualitatively distinct signaling dynamics and phenotypic outcome. Negative feedback regulators promote heterogeneous signaling, as a SMAD7 knock-out specifically affected the signal duration in a subpopulation of cells. Taken together, we propose a quantitative framework that allows predicting and testing sources of cellular signaling heterogeneity.

Universal signal generator for dynamic cell stimulation

Dynamic cell stimulation is a powerful technique for probing gene networks and for applications in stem cell differentiation, immunomodulation and signaling. We developed a robust and flexible method and associated microfluidic devices to generate a wide-range of precisely formulated dynamic chemical signals to stimulate live cells and measure their dynamic response. This signal generator is capable of digital to analog conversion (DAC) through combinatoric selection of discrete input concentrations, and outperforms existing methods by both achievable resolution, dynamic range and simplicity in design. It requires no calibration, has minimal space requirements and can be easily integrated into microfluidic cell culture devices. The signal generator hardware and software we developed allows to choose the waveform, period and amplitude of chemical input signals and features addition of well-defined chemical noise to study the role of stochasticity in cellular information processing.

Computation and measurement of cell decision making errors using single cell data

In this study a new computational method is developed to quantify decision making errors in cells, caused by noise and signaling failures. Analysis of tumor necrosis factor (TNF) signaling pathway which regulates the transcription factor Nuclear Factor κB (NF-κB) using this method identifies two types of incorrect cell decisions called false alarm and miss. These two events represent, respectively, declaring a signal which is not present and missing a signal that does exist. Using single cell experimental data and the developed method, we compute false alarm and miss error probabilities in wild-type cells and provide a formulation which shows how these metrics depend on the signal transduction noise level. We also show that in the presence of abnormalities in a cell, decision making processes can be significantly affected, compared to a wild-type cell, and the method is able to model and measure such effects. In the TNF—NF-κB pathway, the method computes and reveals changes in false alarm and miss probabilities in A20-deficient cells, caused by cell’s inability to inhibit TNF-induced NF-κB response. In biological terms, a higher false alarm metric in this abnormal TNF signaling system indicates perceiving more cytokine signals which in fact do not exist at the system input, whereas a higher miss metric indicates that it is highly likely to miss signals that actually exist. Overall, this study demonstrates the ability of the developed method for modeling cell decision making errors under normal and abnormal conditions, and in the presence of transduction noise uncertainty. Compared to the previously reported pathway capacity metric, our results suggest that the introduced decision error metrics characterize signaling failures more accurately. This is mainly because while capacity is a useful metric to study information transmission in signaling pathways, it does not capture the overlap between TNF-induced noisy response curves.

Cell continuously receives signals from the surrounding environment and is supposed to make correct decisions, i.e., respond properly to various signals and initiate certain cellular functions. Modeling and quantification of decision making processes in a cell have emerged as important areas of research in recent years. Due to signal transduction noise, cells respond differently to similar inputs, which may result in incorrect cell decisions. Here we develop a novel method for characterization of decision making processes in cells, using statistical signal processing and decision theory concepts. To demonstrate the utility of the method, we apply it to an important signaling pathway that regulates molecules which play key roles in cell survival. Our method reveals that cells can make two types of incorrect decisions, namely, false alarm and miss events. We measure the likelihood of these decisions using single cell experimental data, and demonstrate how these incorrect decisions are related to the signal transduction noise or absence of certain molecular functions. Using our method, decision making errors in other molecular systems can be modeled. Such models are useful for understanding and developing treatments for pathological processes such as inflammation, various cancers and autoimmune diseases.

Determining the Limitations and Benefits of Noise in Gene Regulation and Signal Transduction through Single Cell, Microscopy-Based Analysis

Stochastic fluctuations, termed "noise," in the level of biological molecules can greatly impact cellular functions. While biological noise can sometimes be detrimental, recent studies have provided an increasing number of examples in which biological noise can be functionally beneficial. Rather than provide an exhaustive review of the growing literature in this field, in this review, we focus on single-cell studies based on quantitative microscopy that have generated a deeper understanding of the sources, characteristics, limitations, and benefits of biological noise. Specifically, we highlight studies showing how noise can help coordinate the expression of multiple downstream target genes, impact the channel capacity of signaling networks, and interact synergistically with oscillatory dynamics to enhance the sensitivity of signal processing. We conclude with a discussion of current challenges and future opportunities.

Distinct cellular states determine calcium signaling response

The heterogeneity in mammalian cells signaling response is largely a result of pre‐existing cell‐to‐cell variability. It is unknown whether cell‐to‐cell variability rises from biochemical stochastic fluctuations or distinct cellular states. Here, we utilize calcium response to adenosine trisphosphate as a model for investigating the structure of heterogeneity within a population of cells and analyze whether distinct cellular response states coexist. We use a functional definition of cellular state that is based on a mechanistic dynamical systems model of calcium signaling. Using Bayesian parameter inference, we obtain high confidence parameter value distributions for several hundred cells, each fitted individually. Clustering the inferred parameter distributions revealed three major distinct cellular states within the population. The existence of distinct cellular states raises the possibility that the observed variability in response is a result of structured heterogeneity between cells. The inferred parameter distribution predicts, and experiments confirm that variability in IP3R response explains the majority of calcium heterogeneity. Our work shows how mechanistic models and single‐cell parameter fitting can uncover hidden population structure and demonstrate the need for parameter inference at the single‐cell level.

Information processing in bacteria: memory, computation, and statistical physics: a key issues review

Living systems have to constantly sense their external environment and adjust their internal state in order to survive and reproduce. Biological systems, from as complex as the brain to a single E. coli cell, have to process these data in order to make appropriate decisions. How do biological systems sense external signals? How do they process the information? How do they respond to signals? Through years of intense study by biologists, many key molecular players and their interactions have been identified in different biological machineries that carry out these signaling functions. However, an integrated, quantitative understanding of the whole system is still lacking for most cellular signaling pathways, not to say the more complicated neural circuits. To study signaling processes in biology, the key thing to measure is the input-output relationship. The input is the signal itself, such as chemical concentration, external temperature, light (intensity and frequency), and more complex signals such as the face of a cat. The output can be protein conformational changes and covalent modifications (phosphorylation, methylation, etc), gene expression, cell growth and motility, as well as more complex output such as neuron firing patterns and behaviors of higher animals. Due to the inherent noise in biological systems, the measured input-output dependence is often noisy. These noisy data can be analysed by using powerful tools and concepts from information theory such as mutual information, channel capacity, and the maximum entropy hypothesis. This information theory approach has been successfully used to reveal the underlying correlations between key components of biological networks, to set bounds for network performance, and to understand possible network architecture in generating observed correlations. Although the information theory approach provides a general tool in analysing noisy biological data and may be used to suggest possible network architectures in preserving information, it does not reveal the underlying mechanism that leads to the observed input-output relationship, nor does it tell us much about which information is important for the organism and how biological systems use information to carry out specific functions. To do that, we need to develop models of the biological machineries, e.g. biochemical networks and neural networks, to understand the dynamics of biological information processes. This is a much more difficult task. It requires deep knowledge of the underlying biological network-the main players (nodes) and their interactions (links)-in sufficient detail to build a model with predictive power, as well as quantitative input-output measurements of the system under different perturbations (both genetic variations and different external conditions) to test the model predictions to guide further development of the model. Due to the recent growth of biological knowledge thanks in part to high throughput methods (sequencing, gene expression microarray, etc) and development of quantitative in vivo techniques such as various florescence technology, these requirements are starting to be realized in different biological systems. The possible close interaction between quantitative experimentation and theoretical modeling has made systems biology an attractive field for physicists interested in quantitative biology. In this review, we describe some of the recent work in developing a quantitative predictive model of bacterial chemotaxis, which can be considered as the hydrogen atom of systems biology. Using statistical physics approaches, such as the Ising model and Langevin equation, we study how bacteria, such as E. coli, sense and amplify external signals, how they keep a working memory of the stimuli, and how they use these data to compute the chemical gradient. In particular, we will describe how E. coli cells avoid cross-talk in a heterogeneous receptor cluster to keep a ligand-specific memory. We will also study the thermodynamic costs of adaptation for cells to maintain an accurate memory. The statistical physics based approach described here should be useful in understanding design principles for cellular biochemical circuits in general.

Redefining Signaling Pathways with an Expanding Single-Cell Toolbox

Genetically identical cells respond heterogeneously to uniform environmental stimuli. Consequently, investigating the signaling networks that control these cell responses using 'average' bulk cell measurements can obscure underlying mechanisms and misses information emerging from cell-to-cell variability. Here we review recent technological advances including live-cell fluorescence imaging-based approaches and microfluidic devices that enable measurements of signaling networks, dynamics, and responses in single cells. We discuss how these single-cell tools have uncovered novel mechanistic insights for canonical signaling pathways that control cell proliferation (ERK), DNA-damage responses (p53), and innate immune and stress responses (NF-κB). Future improvements in throughput and multiplexing, analytical pipelines, and in vivo applicability will all significantly expand the biological information gained from single-cell measurements of signaling pathways.

Dynamics of simple gene-network motifs subject to extrinsic fluctuations

Cellular processes do not follow deterministic rules; even in identical environments genetically identical cells can make random choices leading to different phenotypes. This randomness originates from fluctuations present in the biomolecular interaction networks. Most previous work has been focused on the intrinsic noise (IN) of these networks. Yet, especially for high-copy-number biomolecules, extrinsic or environmental noise (EN) has been experimentally shown to dominate the variation. Here, we develop an analytical formalism that allows for calculation of the effect of EN on gene-expression motifs. We introduce a method for modeling bounded EN as an auxiliary species in the master equation. The method is fully generic and is not limited to systems with small EN magnitudes. We focus our study on motifs that can be viewed as the building blocks of genetic switches: a nonregulated gene, a self-inhibiting gene, and a self-promoting gene. The role of the EN properties (magnitude, correlation time, and distribution) on the statistics of interest are systematically investigated, and the effect of fluctuations in different reaction rates is compared. Due to its analytical nature, our formalism can be used to quantify the effect of EN on the dynamics of biochemical networks and can also be used to improve the interpretation of data from single-cell gene-expression experiments.