Extrinsic Noise Sources Research Articles

MITOCHONDRIAL MEMBRANE POTENTIAL IS A FUNCTIONALLY RELEVANT AXIS OF NON-GENETIC CELLULAR HETEROGENEITY IN GLIOBLASTOMA

Abstract AIMS Glioma stem cells (GSCs) are believed to underpin treatment resistance in glioblastoma by virtue of their self- renewal capabilities and presumed transcriptional plasticity. Understanding how cell state diversity is established and maintained is crucial to make therapeutic gains. We have previously shown mitochondrial membrane potential (MMP) to be a functionally relevant source of extrinsic noise in embryonic and haematopoietic stem cells. This study evaluates cellular MMP as an axis of variability in GSCs. METHOD MMP was measured by flow cytometry in patient-derived GSC lines using cationic dyes that diffuse reversibly across the mitochondrial membrane in a voltage dependent manner. MMP-high and low populations (top and bottom 10-20%) were fractionated and subjected to RNA-sequencing and assays of proliferation and clonogenicity. Correlation between MMP and global transcription rate was investigated through a uridine analogue (5-EU) incorporation assay. The relationship between MMP and quiescence was assessed, with quiescence defined as inducible histone2B-GFP label retention after 10 days. Timecourse data for MMP was obtained through sequential staining. RESULTS RNA sequencing identified differential gene expression and exon utilization according to MMP status. MMP- high cells upregulated cell cycle genes, while MMP-low cells exhibited a diverse signature suggestive of a more differentiated state. A greater proportion of MMP-high cells were in cycle, but MMP-low cells formed more colonies. MMP positively correlated with global transcription rate in both cycling and quiescent GSCs. Time- course experiments revealed dynamic periodicity in cellular MMP. CONCLUSION The MMP axis reveals transcriptional and functional heterogeneity in GSCs and importantly unmasks phenotypic variability within the treatment-refractory quiescent compartment. The positive correlation between MMP and transcription rate, along with splicing differences, suggests a mechanism underlying functional diversity. Given the oscillatory dynamics of MMP, we postulate that stable-low MMP may define a deeply quiescent, therapy-resistant state. Evaluating MMP as a tractable regulator of GSC fate is warranted.

Range expansions across landscapes with quenched noise

When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also significantly influence the competition between subpopulations vying for space. Little is known about the interplay of these intrinsic and extrinsic sources of noise in population dynamics: When does environmental heterogeneity dominate over genetic drift or vice versa, and what distinguishes their population genetics signatures? Here, in the context of neutral evolution, we examine the interplay between a population's intrinsic, demographic noise and an extrinsic, quenched random noise provided by a heterogeneous environment. Using a multispecies Eden model, we simulate a population expanding over a landscape with random variations in local growth rates and measure how this variability affects genealogical tree structure, and thus genetic diversity. We find that, for strong heterogeneity, the genetic makeup of the expansion front is to a great extent predetermined by the set of fastest paths through the environment. The landscape-dependent statistics of these optimal paths then supersede those of the population's intrinsic noise as the main determinant of evolutionary dynamics. Remarkably, the statistics for coalescence of genealogical lineages, derived from those deterministic paths, strongly resemble the statistics emerging from demographic noise alone in uniform landscapes. This cautions interpretations of coalescence statistics and raises new challenges for inferring past population dynamics.

Model-guided design of microRNA-based gene circuits supports precise dosage of transgenic cargoes into diverse primary cells.

To realize the potential of engineered cells in therapeutic applications, transgenes must be expressed within the window of therapeutic efficacy. Differences in copy number and other sources of extrinsic noise generate variance in transgene expression and limit the performance of synthetic gene circuits. In a therapeutic context, supraphysiological expression of transgenes can compromise engineered phenotypes and lead to toxicity. To ensure a narrow range of transgene expression, we design and characterize Compact microRNA-Mediated Attenuator of Noise and Dosage (ComMAND), a single-transcript, microRNA-based incoherent feedforward loop. We experimentally tune the ComMAND output profile, and we model the system to explore additional tuning strategies. By comparing ComMAND to two-gene implementations, we highlight the precise control afforded by the single-transcript architecture, particularly at relatively low copy numbers. We show that ComMAND tightly regulates transgene expression from lentiviruses and precisely controls expression in primary human T cells, primary rat neurons, primary mouse embryonic fibroblasts, and human induced pluripotent stem cells. Finally, ComMAND effectively sets levels of the clinically relevant transgenes FMRP1 and FXN within a narrow window. Together, ComMAND is a compact tool well-suited to precisely specify expression of therapeutic cargoes.

Quantifying and correcting bias in transcriptional parameter inference from single-cell data

The snapshot distribution of mRNA counts per cell can be measured using single-molecule fluorescence in situ hybridization or single-cell RNA sequencing. These distributions are often fit to the steady-state distribution of the two-state telegraph model to estimate the three transcriptional parameters for a gene of interest: mRNA synthesis rate, the switching on rate (the on state being the active transcriptional state), and the switching off rate. This model assumes no extrinsic noise, i.e., parameters do not vary between cells, and thus estimated parameters are to be understood as approximating the average values in a population. The accuracy of this approximation is currently unclear. Here, we develop a theory that explains the size and sign of estimation bias when inferring parameters from single-cell data using the standard telegraph model. We find specific bias signatures depending on the source of extrinsic noise (which parameter is most variable across cells) and the mode of transcriptional activity. If gene expression is not bursty then the population averages of all three parameters are overestimated if extrinsic noise is in the synthesis rate; underestimation occurs if extrinsic noise is in the switching on rate; both underestimation and overestimation can occur if extrinsic noise is in the switching off rate. We find that some estimated parameters tend to infinity as the size of extrinsic noise approaches a critical threshold. In contrast when gene expression is bursty, we find that in all cases the mean burst size (ratio of the synthesis rate to the switching off rate) is overestimated while the mean burst frequency (the switching on rate) is underestimated. We estimate the size of extrinsic noise from the covariance matrix of sequencing data and use this together with our theory to correct published estimates of transcriptional parameters for mammalian genes.

Out-of-equilibrium gene expression fluctuations in the presence of extrinsic noise

Cell-to-cell variability in protein concentrations is strongly affected by extrinsic noise, especially for highly expressed genes. Extrinsic noise can be due to fluctuations of several possible cellular factors connected to cell physiology and to the level of key enzymes in the expression process. However, how to identify the predominant sources of extrinsic noise in a biological system is still an open question. This work considers a general stochastic model of gene expression with extrinsic noise represented as fluctuations of the different model rates, and focuses on the out-of-equilibrium expression dynamics. Combining analytical calculations with stochastic simulations, we characterize how extrinsic noise shapes the protein variability during gene activation or inactivation, depending on the prevailing source of extrinsic variability, on its intensity and timescale. In particular, we show that qualitatively different noise profiles can be identified depending on which are the fluctuating parameters. This indicates an experimentally accessible way to pinpoint the dominant sources of extrinsic noise using time-coarse experiments.

Scalable and flexible inference framework for stochastic dynamic single-cell models.

Understanding the inherited nature of how biological processes dynamically change over time and exhibit intra- and inter-individual variability, due to the different responses to environmental stimuli and when interacting with other processes, has been a major focus of systems biology. The rise of single-cell fluorescent microscopy has enabled the study of those phenomena. The analysis of single-cell data with mechanistic models offers an invaluable tool to describe dynamic cellular processes and to rationalise cell-to-cell variability within the population. However, extracting mechanistic information from single-cell data has proven difficult. This requires statistical methods to infer unknown model parameters from dynamic, multi-individual data accounting for heterogeneity caused by both intrinsic (e.g. variations in chemical reactions) and extrinsic (e.g. variability in protein concentrations) noise. Although several inference methods exist, the availability of efficient, general and accessible methods that facilitate modelling of single-cell data, remains lacking. Here we present a scalable and flexible framework for Bayesian inference in state-space mixed-effects single-cell models with stochastic dynamic. Our approach infers model parameters when intrinsic noise is modelled by either exact or approximate stochastic simulators, and when extrinsic noise is modelled by either time-varying, or time-constant parameters that vary between cells. We demonstrate the relevance of our approach by studying how cell-to-cell variation in carbon source utilisation affects heterogeneity in the budding yeast Saccharomyces cerevisiae SNF1 nutrient sensing pathway. We identify hexokinase activity as a source of extrinsic noise and deduce that sugar availability dictates cell-to-cell variability.

Clock transitions guard against spin decoherence in singlet fission.

Short coherence times present a primary obstacle in quantum computing and sensing applications. In atomic systems, clock transitions (CTs), formed from avoided crossings in an applied Zeeman field, can substantially increase coherence times. We show how CTs can dampen intrinsic and extrinsic sources of quantum noise in molecules. Conical intersections between two periodic potentials form CTs in electron paramagnetic resonance experiments of the spin-polarized singlet fission photoproduct. We report on a pair of CTs for a two-chromophore molecule in terms of the Zeeman field strength, molecular orientation relative to the field, and molecular geometry.

Mechanobiological conceptual framework for assessing stem cell bioprocess effectiveness.

Fully realizing the enormous potential of stem cells requires developing efficient bioprocesses and optimizations founded in mechanobiological considerations. Here, we emphasize the importance of mechanotransduction as one of the governing principles of stem cell bioprocesses, underscoring the need to further explore the behavioral mechanisms involved in sensing mechanical cues and coordinating transcriptional responses. We identify the sources of intrinsic, extrinsic, and external noise in bioprocesses requiring further study, and discuss the criteria and indicators that may be used to assess and predict cell-to-cell variability resulting from environmental fluctuations. Specifically, we propose a conceptual framework to explain the impact of mechanical forces within the cellular environment, identify key cell state determinants in bioprocesses, and discuss downstream implementation challenges.

Effects of Extrinsic Noise Factors on Machine Learning–Based Chatter Detection in Machining

Abstract Unmitigated chatter can result in poor part quality, accelerated tool wear, and possible damage to spindle and machine. While various methods have been shown to effectively detect chatter, implementation of these methods in noisy environments, such as factory floors, has not been well studied. The present study seeks to explore the effects of extrinsic noise sources on threshold-based and machine learning–based chatter detection methods using audio signals of the machining process. To accomplish this, stable and unstable cuts were made on a milling machine and the audio signal was collected. Data augmentation using Gaussian white noise and periodic noise was conducted to simulate a range of noise levels and types. The performance of these techniques were then compared with respect to the increasing levels of noise. It was found that machine learning–based approaches achieved satisfactory accuracies up to 98.6 % under the presence of extrinsic noise. Conventional static threshold techniques, however, failed under most noise conditions and resulted in false positives depending on the threshold values used. Furthermore, support vector machine approaches demonstrated an ability to classify noisy data despite limited training.

Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations.

The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation-including static extrinsic noise-exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis, a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.

Stochastic Differential Equations for Practical Simulation of Gene Circuits.

The Chemical Langevin Equation approach allows simple stochastic simulation of gene circuits under many practical situations where the number of molecules of the species involved is not extremely low. Here, we describe methods and a computational framework to simulate a population of cells containing gene circuits of interest. These methods account for both intrinsic and extrinsic noise sources, and allow us to have both individual cell-related species and population-related ones. The protocol covers aspects related to proper description of the system and setting the software tools. It also helps to deal with the optimization of data storage and the simulation precision versus computational time issue. Finally, it also gives practical tests to assess the validity of the underlying technical assumptions.

CHARACTERIZATION OF INTRINSIC AND EXTRINSIC NOISE EFFECTS IN POSITIVELY REGULATED GENES

Gene regulation is fundamental for cell survival. This regulation must be both robust to noise and sensitive enough to external stimuli to elicit the proper responses. In this work, we study, through stochastic numerical simulations, how a gene regulatory network with a positive feedback loop responds to environmental changes in the presence of intrinsic and extrinsic noises. Noise effects were characterized by measuring the statistical differences between two protein time series resulting from identical systems subject to the same source of extrinsic noise. A robust analysis was implemented by modifying the kinetic system parameters. We found that the common source of time-varying extrinsic fluctuations leads to a correlation in the systems it affects. The correlation and the extrinsic and intrinsic noise components are modulated by the update period and noise intensity parameters. Our results suggest that noise perception is controlled through the parameters associated with the response time: degradation rates and promoter dissociation constant.

Desynchronization of the molecular clock contributes to the heterogeneity of the inflammatory response.

Heterogeneity in the behavior of genetically and developmentally equivalent cells is becoming increasingly appreciated. There are several sources of cellular heterogeneity, including both intrinsic and extrinsic noise. We found that some aspects of heterogeneity in the response of macrophages to bacterial lipopolysaccharide (LPS) were due to intercellular desynchronization of the molecular clock, a cell-intrinsic oscillator. We found that the ratio of the relative expression of two clock genes, Nfil3 and Dbp, expressed in opposite phases of the clock, determined the fraction of cells that produced the cytokine IL-12p40 in response to LPS. The clock can be entrained by various environmental stimuli, making it a mechanism by which population-level heterogeneity and the inflammatory response can be regulated.

Effects of Zygosity on Stochastic Gene Expression of Diploid Cells

Stochastic gene expression has been extensively studied in natural and synthetic gene expression systems. However, the majority of those contributions, if not all, were concentrated on the haploid systems, where a single allele is inherited by asexual reproduction. Largely left unexplored is the question of how much the allelic imbalance in chromatin accessibility or divergence in transcription factor binding sites would impact the organismal fitness and thus shaped the sequence evolution. Here, we explicitly consider diploid systems with homo- and heterozygous combination of alleles in the regulatory sequences rather than the primary coding sequence and characterize the genetic noise profiles associated with the zygosity. In particular, we show that the heterozygosity may arise as an outcome of evolutionary selection, when the regulatory proteins are subject to stochastic fluctuations, acting as a source of extrinsic noise. Based on this buffering mechanism in heterozygote, we discuss the relevance of our results to the recent reports on the balancing selection enriched in the cis-regulatory sequences of immune cells and epithelial cells.

Suppression of Intensity and Frequency Noise at Low-Sensitivity Operating Points of Period-One Dynamics of Optically Injected Semiconductor Lasers

Period-one (P1) dynamics induced by an optically injected semiconductor laser oscillate at microwave frequencies. The oscillation frequency of a P1 dynamic can be rendered nearly insensitive to small-signal parameter fluctuations and intrinsic laser noise at appropriate operating conditions of the master and slave lasers. In this paper, the noise-canceling properties of the various low-sensitivity (LS) operating points is demonstrated through their dependency on the noise fluctuation frequency and power. The three different types of LS operating points show their effectiveness in suppressing not only P1 intensity and frequency fluctuations caused by narrowband laser perturbations but also intensity and frequency noise caused by broadband intrinsic and extrinsic noise sources.

Single Live Cell Monitoring of Protein Turnover Reveals Intercellular Variability and Cell-Cycle Dependence of Degradation Rates

Cells need to reliably control their proteome composition to maintain homeostasis and regulate growth. How protein synthesis and degradation interplay to control protein expression levels remains unclear. Here, we combined a tandem fluorescent timer and pulse-chase protein labeling to disentangle how protein synthesis and degradation control protein homeostasis in single live mouse embryonic stem cells. We discovered substantial cell-cycle dependence in protein synthesis rates and stabilization of a large number of proteins around cytokinesis. Protein degradation rates were highly variable between cells, co-varied within individual cells for different proteins, and were positively correlated with synthesis rates. This suggests variability in proteasome activity as an important source of global extrinsic noise in gene expression. Our approach paves the way toward understanding the complex interplay of synthesis and degradation processes in determining protein levels of individual mammalian cells.

Stochastic sequestration dynamics: a minimal model with extrinsic noise for bimodal distributions and competitors correlation

Many biological processes are known to be based on molecular sequestration. This kind of dynamics involves two types of molecular species, namely targets and sequestrants, that bind to form a complex. In the simple framework of mass-action law, key features of these systems appear to be threshold-like profiles of the amounts of free molecules as a function of the parameters determining their possible maximum abundance. However, biochemical processes are probabilistic and take place in stochastically fluctuating environments. How these different sources of noise affect the final outcome of the network is not completely characterised yet. In this paper we specifically investigate the effects induced by a source of extrinsic noise onto a minimal stochastic model of molecular sequestration. We analytically show how bimodal distributions of the targets can appear and characterise them as a result of noise filtering mediated by the threshold response. We then address the correlations between target species induced by the sequestrant and discuss how extrinsic noise can turn the negative correlation caused by competition into a positive one. Finally, we consider the more complex scenario of competitive inhibition for enzymatic kinetics and discuss the relevance of our findings with respect to applications.

Low-frequency magnetic sensing by magnetoelectric metglas/bidomain LiNbO3 long bars

We present an investigation into the magnetic sensing performance of magnetoelectric bilayered metglas/bidomain LiNbO3 long thin bars operating in a cantilever or free vibrating regime and under quasi-static and low-frequency resonant conditions. Bidomain single crystals of Y + 128°-cut LiNbO3 were engineered by an improved diffusion annealing technique with a polarization macrodomain structure of the ‘head-to-head’ and ‘tail-to-tail’ type. Long composite bars with lengths of 30, 40 and 45 mm, as well as with and without attached small tip proof masses, were studied. ME coefficients as large as 550 V (cm · Oe)−1, corresponding to a conversion ratio of 27.5 V Oe−1, were obtained under resonance conditions at frequencies of the order of 100 Hz in magnetic bias fields as low as 2 Oe. Equivalent magnetic noise spectral densities down to 120 pT Hz−1/2 at 10 Hz and to 68 pT Hz−1/2 at a resonance frequency as low as 81 Hz were obtained for the 45 mm long cantilever bar with a tip proof mass of 1.2 g. In the same composite without any added mass the magnetic noise was shown to be as low as 37 pT Hz−1/2 at a resonance frequency of 244 Hz and 1.2 pT Hz−1/2 at 1335 Hz in a fixed cantilever and free vibrating regimes, respectively. A simple unidimensional dynamic model predicted the possibility to drop the low-frequency magnetic noise by more than one order of magnitude in case all the extrinsic noise sources are suppressed, especially those related to external vibrations, and the thickness ratio of the magnetic-to-piezoelectric phases is optimized. Thus, we have shown that such systems might find use in simple and sensitive room-temperature low-frequency magnetic sensors, e.g. for biomedical applications.

Careful accounting of extrinsic noise in protein expression reveals correlations among its sources.

In order to grow and replicate, living cells must express a diverse array of proteins, but the process by which proteins are made includes a great deal of inherent randomness. Understanding this randomness-whether it arises from the discrete stochastic nature of chemical reactivity ("intrinsic" noise), or from cell-to-cell variability in the concentrations of molecules involved in gene expression, or from the timings of important cell-cycle events like DNA replication and cell division ("extrinsic" noise)-remains a challenge. In this article we analyze a model of gene expression that accounts for several extrinsic sources of noise, including those associated with chromosomal replication, cell division, and variability in the numbers of RNA polymerase, ribonuclease E, and ribosomes. We then attempt to fit our model to a large proteomics and transcriptomics data set and find that only through the introduction of a few key correlations among the extrinsic noise sources can we accurately recapitulate the experimental data. These include significant correlations between the rate of mRNA degradation (mediated by ribonuclease E) and the rates of both transcription (RNA polymerase) and translation (ribosomes) and, strikingly, an anticorrelation between the transcription and the translation rates themselves.

Estimation Methods of the Point Spread Function Axial Position: A Comparative Computational Study

The precise knowledge of the point spread function is central for any imaging system characterization. In fluorescence microscopy, point spread function (PSF) determination has become a common and obligatory task for each new experimental device, mainly due to its strong dependence on acquisition conditions. During the last decade, algorithms have been developed for the precise calculation of the PSF, which fit model parameters that describe image formation on the microscope to experimental data. In order to contribute to this subject, a comparative study of three parameter estimation methods is reported, namely: I-divergence minimization (MIDIV), maximum likelihood (ML) and non-linear least square (LSQR). They were applied to the estimation of the point source position on the optical axis, using a physical model. Methods’ performance was evaluated under different conditions and noise levels using synthetic images and considering success percentage, iteration number, computation time, accuracy and precision. The main results showed that the axial position estimation requires a high SNR to achieve an acceptable success level and higher still to be close to the estimation error lower bound. ML achieved a higher success percentage at lower SNR compared to MIDIV and LSQR with an intrinsic noise source. Only the ML and MIDIV methods achieved the error lower bound, but only with data belonging to the optical axis and high SNR. Extrinsic noise sources worsened the success percentage, but no difference was found between noise sources for the same method for all methods studied.