Single-cell responses to ionizing radiation

While gene expression studies have proved extremely important in understanding cellular processes, it is becoming more apparent that there may be differences in individual cells that are missed by studying the population as a whole. We have developed a qRT-PCR protocol that allows us to assay multiple gene products in small samples, starting at 100 cells and going down to a single cell, and have used it to study radiation responses at the single-cell level. Since the accuracy of qRT-PCR depends greatly on the choice of “housekeeping” genes used for normalization, initial studies concentrated on determining the optimal panel of such genes. Using an endogenous control array, it was found that for IMR90 cells, common housekeeping genes tend to fall into one of two categories—those that are relatively stably expressed regardless of the number of cells in the sample, e.g., B2M, PPIA, and GAPDH, and those that are more variable (again regardless of the size of the population), e.g., YWHAZ, 18S, TBP, and HPRT1. Further, expression levels in commonly studied radiation-response genes, such as ATF3, CDKN1A, GADD45A, and MDM2, were assayed in 100, 10, and single-cell samples. It is here that the value of single-cell analyses becomes apparent. It was observed that the expression of some genes such as FGF2 and MDM2 was relatively constant over all irradiated cells, while that of others such as FAS was considerably more variable. It was clear that almost all cells respond to ionizing radiation but the individual responses were considerably varied. The analyses of single cells indicate that responses in individual cells are not uniform and suggest that responses observed in populations are not indicative of identical patterns in all cells. This in turn points to the value of single-cell analyses.     

Genetic noise control via protein oligomerization

Background

Biochemical equilibria are usually modeled iteratively: given one or a few fitted models, if there is a lack of fit or over fitting, a new model with additional or fewer parameters is then fitted, and the process is repeated. The problem with this approach is that different analysts can propose and select different models and thus extract different binding parameter estimates from the same data. An alternative is to first generate a comprehensive standardized list of plausible models, and to then fit them exhaustively, or semi-exhaustively.

Results

A framework is presented in which equilibriums are modeled as pairs (g, h) where g = 0 maps total reactant concentrations (system inputs) into free reactant concentrations (system states) which h then maps into expected values of measurements (system outputs). By letting dissociation constants K _d be either freely estimated, infinity, zero, or equal to other K _d , and by letting undamaged protein fractions be either freely estimated or 1, many g models are formed. A standard space of g models for ligand-induced protein dimerization equilibria is given. Coupled to an h model, the resulting (g, h) were fitted to dTTP induced R1 dimerization data (R1 is the large subunit of ribonucleotide reductase). Models with the fewest parameters were fitted first. Thereafter, upon fitting a batch, the next batch of models (with one more parameter) was fitted only if the current batch yielded a model that was better (based on the Akaike Information Criterion) than the best model in the previous batch (with one less parameter). Within batches models were fitted in parallel. This semi-exhaustive approach yielded the same best models as an exhaustive model space fit, but in approximately one-fifth the time.

Conclusion

Comprehensive model space based biochemical equilibrium model selection methods are realizable. Their significance to systems biology as mappings of data into mathematical models warrants their development.     

From intracellular signaling to population oscillations: bridging size- and time-scales in collective behavior

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems, we know that behavioral changes in the individual constituents of a collectively behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here, we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.     

The inbreeding effective number and the effective number of alleles in a population that varies in size

Consider a population that does not change in size. If it is assumed that there are an infinite number of possible neutral alleles at a locus and u is the probability that a particular gene mutates to some other gene in one generation, the effective number of alleles n_e is computed to be 4N_eu + 1, where N_e is the inbreeding effective population number. It is assumed in this paper that the number of individuals in a monoecious population, or the numbers of males and females in a dioecious population, are states in a finite irreducible Markov chain. In general it is impossible to obtain a single value of n_e. In some cases where the computation of n_e is possible, the results are as follows. When the population is monoecious, N_e is the reciprocal of the asymptotic average, over population sizes, of the probabilities that two gametes uniting to form an individual came from the same individual one generation earlier. In dioecious populations, N_e is the reciprocal of the long-run average of the probabilities that two homologous genes in separate individuals of one generation came from the same individual one generation earlier. Special cases are discussed.     

Experimental verification of the behavioral foundation of bacterial transport parameters using microfluidics

We present novel microfluidic experiments to quantify population-scale transport parameters (chemotactic sensitivity χ₀ and random motility μ) of a population of bacteria. Previously, transport parameters have been derived theoretically from single-cell swimming behavior using probabilistic models, yet the mechanistic foundations of this upscaling process have not been verified experimentally. We designed a microfluidic capillary assay to generate and accurately measure gradients of chemoattractant (α-methylaspartate) while simultaneously capturing the swimming trajectories of individual Escherichia coli bacteria using videomicroscopy and cell tracking. By measuring swimming speed and bias in the swimming direction of single cells for a range of chemoattractant concentrations and concentration gradients, we directly computed the chemotactic velocity V_C and the associated chemotactic sensitivity χ₀. We then show how μ can also be readily determined using microfluidics but that a population-scale microfluidic approach is experimentally more convenient than a single-cell analysis in this case. Measured values of both χ₀ [(12.4 ± 2.0) × 10⁻⁴ cm² s⁻¹] and μ [(3.3 ± 0.8) × 10⁻⁶ cm² s⁻¹] are comparable to literature results. This microscale approach to bacterial chemotaxis lends experimental support to theoretical derivations of population-scale transport parameters from single-cell behavior. Furthermore, this study shows that microfluidic platforms can go beyond traditional chemotaxis assays and enable the quantification of bacterial transport parameters.     

Identity Coefficients in Finite Populations. I. Evolution of Identity Coefficients in a Random Mating Diploid Dioecious Population

Properties of identity relation between genes are discussed, and a derivation of recurrent equations of identity coefficients in a random mating, diploid dioecious population is presented. Computations are run by repeated matrix multiplication. Results show that for effective population size (N_e) larger than 16 and no mutation, a given identity coefficient at any time t can be expressed approximately as a function of (1—f), (1—f)³ and (1— f)⁶, where f is the mean inbreeding coefficient at time t. Tables are presented, for small N_e values and extreme sex ratios, showing the pattern of change in the identity coefficients over time. The pattern of evolution of identity coefficients is also presented and discussed with respect to N _eu, where u is the mutation rate. Applications of these results to the evolution of genetic variability within and between inbred lines are discussed.     

Subpopulations of sensorless bacteria drive fitness in fluctuating environments

Populations of bacteria often undergo a lag in growth when switching conditions. Because growth lags can be large compared to typical doubling times, variations in growth lag are an important but often overlooked component of bacterial fitness in fluctuating environments. We here explore how growth lag variation is determined for the archetypical switch from glucose to lactose as a carbon source in Escherichia coli. First, we show that single-cell lags are bimodally distributed and controlled by a single-molecule trigger. That is, gene expression noise causes the population before the switch to divide into subpopulations with zero and nonzero lac operon expression. While “sensorless” cells with zero preexisting lac expression at the switch have long lags because they are unable to sense the lactose signal, any nonzero lac operon expression suffices to ensure a short lag. Second, we show that the growth lag at the population level depends crucially on the fraction of sensorless cells and that this fraction in turn depends sensitively on the growth condition before the switch. Consequently, even small changes in basal expression can significantly affect the fraction of sensorless cells, thereby population lags and fitness under switching conditions, and may thus be subject to significant natural selection. Indeed, we show that condition-dependent population lags vary across wild E. coli isolates. Since many sensory genes are naturally low expressed in conditions where their inducer is not present, bimodal responses due to subpopulations of sensorless cells may be a general mechanism inducing phenotypic heterogeneity and controlling population lags in switching environments. This mechanism also illustrates how gene expression noise can turn even a simple sensory gene circuit into a bet hedging module and underlines the profound role of gene expression noise in regulatory responses.

Is ignorance bliss for some bacterial cells? Single-cell analysis of the archetypical switch from glucose to lactose as a carbon source in E. coli shows that bacteria can exhibit stochastic bimodal responses to external stimuli because the corresponding sensory circuit is so lowly expressed that some cells are effectively blind to the stimulus.     

Optimal transport analysis reveals trajectories in steady-state systems

Understanding how cells change their identity and behaviour in living systems is an important question in many fields of biology. The problem of inferring cell trajectories from single-cell measurements has been a major topic in the single-cell analysis community, with different methods developed for equilibrium and non-equilibrium systems (e.g. haematopoeisis vs. embryonic development). We show that optimal transport analysis, a technique originally designed for analysing time-courses, may also be applied to infer cellular trajectories from a single snapshot of a population in equilibrium. Therefore, optimal transport provides a unified approach to inferring trajectories that is applicable to both stationary and non-stationary systems. Our method, StationaryOT, is mathematically motivated in a natural way from the hypothesis of a Waddington’s epigenetic landscape. We implement StationaryOT as a software package and demonstrate its efficacy in applications to simulated data as well as single-cell data from Arabidopsis thaliana root development.     

Optimal tuning of weighted kNN- and diffusion-based methods for denoising single cell genomics data

The analysis of single-cell genomics data presents several statistical challenges, and extensive efforts have been made to produce methods for the analysis of this data that impute missing values, address sampling issues and quantify and correct for noise. In spite of such efforts, no consensus on best practices has been established and all current approaches vary substantially based on the available data and empirical tests. The k-Nearest Neighbor Graph (kNN-G) is often used to infer the identities of, and relationships between, cells and is the basis of many widely used dimensionality-reduction and projection methods. The kNN-G has also been the basis for imputation methods using, e.g., neighbor averaging and graph diffusion. However, due to the lack of an agreed-upon optimal objective function for choosing hyperparameters, these methods tend to oversmooth data, thereby resulting in a loss of information with regard to cell identity and the specific gene-to-gene patterns underlying regulatory mechanisms. In this paper, we investigate the tuning of kNN- and diffusion-based denoising methods with a novel non-stochastic method for optimally preserving biologically relevant informative variance in single-cell data. The framework, Denoising Expression data with a Weighted Affinity Kernel and Self-Supervision (DEWÄKSS), uses a self-supervised technique to tune its parameters. We demonstrate that denoising with optimal parameters selected by our objective function (i) is robust to preprocessing methods using data from established benchmarks, (ii) disentangles cellular identity and maintains robust clusters over dimension-reduction methods, (iii) maintains variance along several expression dimensions, unlike previous heuristic-based methods that tend to oversmooth data variance, and (iv) rarely involves diffusion but rather uses a fixed weighted kNN graph for denoising. Together, these findings provide a new understanding of kNN- and diffusion-based denoising methods. Code and example data for DEWÄKSS is available at https://gitlab.com/Xparx/dewakss/-/tree/Tjarnberg2020branch.     

Parameter inference for stochastic biochemical models from perturbation experiments parallelised at the single cell level

Understanding and characterising biochemical processes inside single cells requires experimental platforms that allow one to perturb and observe the dynamics of such processes as well as computational methods to build and parameterise models from the collected data. Recent progress with experimental platforms and optogenetics has made it possible to expose each cell in an experiment to an individualised input and automatically record cellular responses over days with fine time resolution. However, methods to infer parameters of stochastic kinetic models from single-cell longitudinal data have generally been developed under the assumption that experimental data is sparse and that responses of cells to at most a few different input perturbations can be observed. Here, we investigate and compare different approaches for calculating parameter likelihoods of single-cell longitudinal data based on approximations of the chemical master equation (CME) with a particular focus on coupling the linear noise approximation (LNA) or moment closure methods to a Kalman filter. We show that, as long as cells are measured sufficiently frequently, coupling the LNA to a Kalman filter allows one to accurately approximate likelihoods and to infer model parameters from data even in cases where the LNA provides poor approximations of the CME. Furthermore, the computational cost of filtering-based iterative likelihood evaluation scales advantageously in the number of measurement times and different input perturbations and is thus ideally suited for data obtained from modern experimental platforms. To demonstrate the practical usefulness of these results, we perform an experiment in which single cells, equipped with an optogenetic gene expression system, are exposed to various different light-input sequences and measured at several hundred time points and use parameter inference based on iterative likelihood evaluation to parameterise a stochastic model of the system.     

Human C-kit+CD45− cardiac stem cells are heterogeneous and display both cardiac and endothelial commitment by single-cell qPCR analysis

C-kit expressing cardiac stem cells have been described as multipotent. We have previously identified human cardiac C-kit+CD45− cells, but only found evidence of endothelial commitment. A small cardiac committed subpopulation within the C-kit+CD45− population might however be present. To investigate this at single-cell level, right and left atrial biopsies were dissociated and analyzed by FACS. Only right atrial biopsies contained a clearly distinguishable C-kit+CD45− population, which was single-cell sorted for qPCR. A minor portion of the sorted cells (1.1%) expressed early cardiac gene NKX2.5 while most of the cells (81%) expressed late endothelial gene VWF. VWF− cells were analyzed for a wider panel of genes. One group of these cells expressed endothelial genes (FLK-1, CD31) while another group expressed late cardiac genes (TNNT2, ACTC1). In conclusion, human C-kit+CD45− cells were predominantly localized to the right atrium. While most of these cells expressed endothelial genes, a minor portion expressed cardiac genes.     

Approximate Bayesian estimation of extinction rate in the Finnish Daphnia magna metapopulation

Approximate Bayesian computation (ABC) is useful for parameterizing complex models in population genetics. In this study, ABC was applied to simultaneously estimate parameter values for a model of metapopulation coalescence and test two alternatives to a strict metapopulation model in the well‐studied network of Daphnia magna populations in Finland. The models shared four free parameters: the subpopulation genetic diversity (θ_S), the rate of gene flow among patches (4Nm), the founding population size (N₀) and the metapopulation extinction rate (e) but differed in the distribution of extinction rates across habitat patches in the system. The three models had either a constant extinction rate in all populations (strict metapopulation), one population that was protected from local extinction (i.e. a persistent source), or habitat‐specific extinction rates drawn from a distribution with specified mean and variance. Our model selection analysis favoured the model including a persistent source population over the two alternative models. Of the closest 750 000 data sets in Euclidean space, 78% were simulated under the persistent source model (estimated posterior probability = 0.769). This fraction increased to more than 85% when only the closest 150 000 data sets were considered (estimated posterior probability = 0.774). Approximate Bayesian computation was then used to estimate parameter values that might produce the observed set of summary statistics. Our analysis provided posterior distributions for e that included the point estimate obtained from previous data from the Finnish D. magna metapopulation. Our results support the use of ABC and population genetic data for testing the strict metapopulation model and parameterizing complex models of demography.     

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.     

Single Cell Visualization of Yeast Gene Expression Shows Correlation of Epigenetic Switching between Multiple Heterochromatic Regions through Multiple Generations

Differences in gene expression between individual cells can be mediated by epigenetic regulation; thus, methods that enable detailed analyses of single cells are crucial to understanding this phenomenon. In this study, genomic silencing regions of Saccharomyces cerevisiae that are subject to epigenetic regulation, including the HMR, HML, and telomere regions, were investigated using a newly developed single cell analysis method. This method uses fluorescently labeled proteins to track changes in gene expression over multiple generations of a single cell. Epigenetic control of gene expression differed depending on the specific silencing region at which the reporter gene was inserted. Correlations between gene expression at the HMR-left and HMR-right regions, as well as the HMR-right and HML-right regions, were observed in the single-cell level; however, no such correlations involving the telomere region were observed. Deletion of the histone acetyltransferase GCN5 gene from a yeast strain carrying a fluorescent reporter gene at the HMR-left region reduced the frequency of changes in gene expression over a generation. The results presented here suggest that epigenetic control within an individual cell is reversible and can be achieved via regulation of histone acetyltransferase activity.     

Insights into Penicillium roqueforti Morphological and Genetic Diversity

Fungi exhibit substantial morphological and genetic diversity, often associated with cryptic species differing in ecological niches. Penicillium roqueforti is used as a starter culture for blue-veined cheeses, being responsible for their flavor and color, but is also a common spoilage organism in various foods. Different types of blue-veined cheeses are manufactured and consumed worldwide, displaying specific organoleptic properties. These features may be due to the different manufacturing methods and/or to the specific P. roqueforti strains used. Substantial morphological diversity exists within P. roqueforti and, although not taxonomically valid, several technological names have been used for strains on different cheeses (e.g., P. gorgonzolae, P. stilton). A worldwide P. roqueforti collection from 120 individual blue-veined cheeses and 21 other substrates was analyzed here to determine (i) whether P. roqueforti is a complex of cryptic species, by applying the Genealogical Concordance Phylogenetic Species Recognition criterion (GC-PSR), (ii) whether the population structure assessed using microsatellite markers correspond to blue cheese types, and (iii) whether the genetic clusters display different morphologies. GC-PSR multi-locus sequence analyses showed no evidence of cryptic species. The population structure analysis using microsatellites revealed the existence of highly differentiated populations, corresponding to blue cheese types and with contrasted morphologies. This suggests that the population structure has been shaped by different cheese-making processes or that different populations were recruited for different cheese types. Cheese-making fungi thus constitute good models for studying fungal diversification under recent selection.