Stochastic Sensitivity Analysis and Kernel Inference via Distributional Data

Cellular processes are noisy due to the stochastic nature of biochemical reactions. As such, it is impossible to predict the exact quantity of a molecule or other attributes at the single-cell level. However, the distribution of a molecule over a population is often deterministic and is governed by the underlying regulatory networks relevant to the cellular functionality of interest. Recent studies have started to exploit this property to infer network states. To facilitate the analysis of distributional data in a general experimental setting, we introduce a computational framework to efficiently characterize the sensitivity of distributional output to changes in external stimuli. Further, we establish a probability-divergence-based kernel regression model to accurately infer signal level based on distribution measurements. Our methodology is applicable to any biological system subject to stochastic dynamics and can be used to elucidate how population-based information processing may contribute to organism-level functionality. It also lays the foundation for engineering synthetic biological systems that exploit population decoding to more robustly perform various biocomputation tasks, such as disease diagnostics and environmental-pollutant sensing.     

Cell Growth and Size Homeostasis in Silico

Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a research work performed by a different group, size distributions of an exponentially growing population of mammalian cells were used to infer cell-growth rate in size. The results suggested that cell growth was neither linear nor exponential, but subject to size-dependent regulation. To explain the observed growth pattern, we built a mathematical model in which growth rate was regulated by the relative amount of mRNA and ribosomes in a cell. Under the growth model and a stochastic division rule, we simulated the evolution of a population of cells. Both the sampled growth rate and size distribution from this in silico population agreed well with experimental data. To explore the model space, alternative growth models and division rules were studied. This work may serve as a starting point to understand the mechanisms behind cell growth and size regulation using predictive models.     

Analysing dynamical behavior of cellular networks via stochastic bifurcations

The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.     

Bistability versus bimodal distributions in gene regulatory processes from population balance

In recent times, stochastic treatments of gene regulatory processes have appeared in the literature in which a cell exposed to a signaling molecule in its environment triggers the synthesis of a specific protein through a network of intracellular reactions. The stochastic nature of this process leads to a distribution of protein levels in a population of cells as determined by a Fokker-Planck equation. Often instability occurs as a consequence of two (stable) steady state protein levels, one at the low end representing the "off" state, and the other at the high end representing the "on" state for a given concentration of the signaling molecule within a suitable range. A consequence of such bistability has been the appearance of bimodal distributions indicating two different populations, one in the "off" state and the other in the "on" state. The bimodal distribution can come about from stochastic analysis of a single cell. However, the concerted action of the population altering the extracellular concentration in the environment of individual cells and hence their behavior can only be accomplished by an appropriate population balance model which accounts for the reciprocal effects of interaction between the population and its environment. In this study, we show how to formulate a population balance model in which stochastic gene expression in individual cells is incorporated. Interestingly, the simulation of the model shows that bistability is neither sufficient nor necessary for bimodal distributions in a population. The original notion of linking bistability with bimodal distribution from single cell stochastic model is therefore only a special consequence of a population balance model.     

Stochastic modeling of gene positive autoregulation networks involving signal molecules

Positive autoregulation in gene regulation networks has been shown in the past to exhibit stochastic behavior, including stochastic bistability, in which an initially uniform cell population develops into two distinct subpopulations. However, positive autoregulation is often mediated by signal molecules, which have not been considered in prior stochastic analysis of these networks. Here we propose both a full model of such a network that includes a signal molecule, and a simplified model in which the signal molecules have been eliminated through the use of two simplifications. The simplified model is amenable to direct mathematical analysis that shows that stochastic bistability is possible. We use stochastic Petri networks for simulating both types of models. The simulation results show that 1), the stochastic behavior of the two models is similar; and 2), that the analytical steady-state distribution of the simplified model matches well the transient results at times equal to that of a cell generation. A discussion of the simplifications we used in the context of the results indicates the importance of the signal molecule number as a factor determining the presence of bistability. This is further supported from a deterministic steady-state analysis of the full model that is shown to be a useful indicator of potential stochastic bistability. We use the regulation of SdiA in Escherichia coli as an example, due to the importance of this protein and of the signal molecule, a bacterial autoinducer, that is involved. However, the use of kinetic parameter values representing typical cellular activities make the conclusions applicable to other signal-mediated positive autoregulation networks as well.     

PCA based population generation for genetic network optimization

A gene regulatory network (GRN) represents a set of genes and its regulatory interactions. The inference of the regulatory interactions between genes is usually carried out using an appropriate mathematical model and the available gene expression profile. Among the various models proposed for GRN inference, our recently proposed Michaelis–Menten based ODE model provides a good trade-off between the computational complexity and biological relevance. This model, like other known GRN models, also uses an evolutionary algorithm for parameter estimation. Considering various issues associated with such population based stochastic optimization approaches (e.g. diversity, premature convergence due to local optima, accuracy, etc.), it becomes important to seed the initial population with good individuals which are closer to the optimal solution. In this paper, we exploit the inherent strength of principal component analysis (PCA) in a novel manner to initialize the population for GRN optimization. The benefit of the proposed method is validated by reconstructing in silico and in vivo networks of various sizes. For the same level of accuracy, the approach with PCA based initialization shows improved convergence speed.     

Plant extinction risk under climate change: are forecast range shifts alone a good indicator of species vulnerability to global warming?

Models that couple habitat suitability with demographic processes offer a potentially improved approach for estimating spatial distributional shifts and extinction risk under climate change. Applying such an approach to five species of Australian plants with contrasting demographic traits, we show that: (i) predicted climate‐driven changes in range area are sensitive to the underlying habitat model, regardless of whether demographic traits and their interaction with habitat patch configuration are modeled explicitly; and (ii) caution should be exercised when using predicted changes in total habitat suitability or geographic extent to infer extinction risk, because the relationship between these metrics is often weak. Measures of extinction risk, which quantify threats to population persistence, are particularly sensitive to life‐history traits, such as recruitment response to fire, which explained approximately 60% of the deviance in expected minimum abundance. Dispersal dynamics and habitat patch structure have the strongest influence on the amount of movement of the trailing and leading edge of the range margin, explaining roughly 40% of modeled structural deviance. These results underscore the need to consider direct measures of extinction risk (population declines and other measures of stochastic viability), as well as measures of change in habitat area, when assessing climate change impacts on biodiversity. Furthermore, direct estimation of extinction risk incorporates important demographic and ecosystem processes, which potentially influence species’ vulnerability to extinction due to climate change.     

Robust Inference of Cell-to-Cell Expression Variations from Single- and K-Cell Profiling

Quantifying heterogeneity in gene expression among single cells can reveal information inaccessible to cell-population averaged measurements. However, the expression level of many genes in single cells fall below the detection limit of even the most sensitive technologies currently available. One proposed approach to overcome this challenge is to measure random pools of k cells (e.g., 10) to increase sensitivity, followed by computational “deconvolution” of cellular heterogeneity parameters (CHPs), such as the biological variance of single-cell expression levels. Existing approaches infer CHPs using either single-cell or k-cell data alone, and typically within a single population of cells. However, integrating both single- and k-cell data may reap additional benefits, and quantifying differences in CHPs across cell populations or conditions could reveal novel biological information. Here we present a Bayesian approach that can utilize single-cell, k-cell, or both simultaneously to infer CHPs within a single condition or their differences across two conditions. Using simulated as well as experimentally generated single- and k-cell data, we found situations where each data type would offer advantages, but using both together can improve precision and better reconcile CHP information contained in single- and k-cell data. We illustrate the utility of our approach by applying it to jointly generated single- and k-cell data to reveal CHP differences in several key inflammatory genes between resting and inflammatory cytokine-activated human macrophages, delineating differences in the distribution of ‘ON’ versus ‘OFF’ cells and in continuous variation of expression level among cells. Our approach thus offers a practical and robust framework to assess and compare cellular heterogeneity within and across biological conditions using modern multiplexed technologies.     

On the study of two interacting populations one of which acts independently of the other

Many ecological and biological systems can be studied in terms of a bivariate stochastic branching process, {X ₁ (t), X ₂ (t)}, each of whose components (or populations) varies in magnitude according to the laws of a generalized birth-death process. Of particular interest is such a model in which the birth and death rates of the first population,X ₁, are constant while those of the second population,X ₂, exhibit a functional dependence upon the magnitude of the first. It is shown, first, that the existence of the stochastic mean of a birth death process implies the existence of all higher moments. The values of all the factorial moments of such a process are then determined. The moments of the dependent population of the bivariate process are given in terms of its expectation and the joint probability density function of the process is determined. It is possible, therefore, to use Bayesian techniques to infer conclusions about the independent population, given information about the variation of the dependent one.     

Cell to Cell Variability of Radiation-Induced Foci: Relation between Observed Damage and Energy Deposition

Most studies that aim to understand the interactions between different types of photon radiation and cellular DNA assume homogeneous cell irradiation, with all cells receiving the same amount of energy. The level of DNA damage is therefore generally determined by averaging it over the entire population of exposed cells. However, evaluating the molecular consequences of a stochastic phenomenon such as energy deposition of ionizing radiation by measuring only an average effect may not be sufficient for understanding some aspects of the cellular response to this radiation. The variance among the cells associated with this average effect may also be important for the behaviour of irradiated tissue. In this study, we accurately estimated the distribution of the number of radiation-induced γH2AX foci (RIF) per cell nucleus in a large population of endothelial cells exposed to 3 macroscopic doses of gamma rays from ⁶⁰Co. The number of RIF varied significantly and reproducibly from cell to cell, with its relative standard deviation ranging from 36% to 18% depending on the macroscopic dose delivered. Interestingly, this relative cell-to-cell variability increased as the dose decreased, contrary to the mean RIF count per cell. This result shows that the dose effect, in terms of the number of DNA lesions indicated by RIF is not as simple as a purely proportional relation in which relative SD is constant with dose. To analyse the origins of this observed variability, we calculated the spread of the specific energy distribution for the different target volumes and subvolumes in which RIF can be generated. Variances, standard deviations and relative standard deviations all changed similarly from dose to dose for biological and calculated microdosimetric values. This similarity is an important argument that supports the hypothesis of the conservation of the association between the number of RIF per nucleus and the specific energy per DNA molecule. This comparison allowed us to calculate a volume of 1.6 μm³ for which the spread of the specific energy distribution could explain the entire variability of RIF counts per cell in an exposed cell population. The definition of this volume may allow to use a microdosimetric quantity to predict heterogeneity in DNA damage. Moreover, this value is consistent with the order of magnitude of the volume occupied by the hydrated sugar-phosphate backbone of the DNA molecule, which is the part of the DNA molecule responsible for strand breaks.     

Heat shock response in CHO mammalian cells is controlled by a nonlinear stochastic process

In many biological systems, the interactions that describe the coupling between different units in a genetic network are nonlinear and stochastic. We study the interplay between stochasticity and nonlinearity using the responses of Chinese hamster ovary (CHO) mammalian cells to different temperature shocks. The experimental data show that the mean value response of a cell population can be described by a mathematical expression (empirical law) which is valid for a large range of heat shock conditions. A nonlinear stochastic theoretical model was developed that explains the empirical law for the mean response. Moreover, the theoretical model predicts a specific biological probability distribution of responses for a cell population. The prediction was experimentally confirmed by measurements at the single-cell level. The computational approach can be used to study other nonlinear stochastic biological phenomena.     

The relationship between mammal faunas and climatic instability since the Last Glacial Maximum: A Nearctic vs. Western Palearctic comparison

Climate has played a key role in shaping the geographic patterns of biodiversity. The imprint of Quaternary climatic fluctuations is particularly evident on the geographic distribution of Holarctic faunas, which dramatically shifted their ranges following the alternation of glacial-interglacial cycles during the Pleistocene. Here, we evaluate the existence of differences between climatically stable and unstable regions – defined on the basis of climatic change velocity since the Last Glacial Maximum – in the geographic distribution of several biological attributes of extant terrestrial mammals of the Nearctic and Western Palearctic regions. Specifically, we use a macroecological approach to assess the dissimilarities in species richness, range size, body size, longevity and litter size of species that inhabit regions with contrasting histories of climatic stability. While several studies have documented how the distributional ranges of animals can be affected by long-term historic climatic fluctuations, there is less evidence on the species-specific traits that determine their responsiveness under such climatic instability. We find that climatically unstable areas have more widespread species and lower mammal richness than stable regions in both continents. We detected stronger signatures of historical climatic instability on the geographic distribution of body size in the Nearctic region, possibly reflecting lagged responses to recolonize deglaciated regions. However, the way that animals respond to climatic fluctuations varies widely among species and we were unable to find a relationship between climatic instability and other mammal life-history traits (longevity and litter size) in any of the two biogeographic regions. We, therefore, conclude that beyond some biological traits typical of macroecological analyses such as geographic range size and body size, it is difficult to infer the responsiveness of species distributions to climate change solely based on particular life-history traits.     

Native range climate is insufficient to predict anuran invasive potential

Niche conservatism explains biological invasions worldwide. However, a plethora of ecological processes may lead invasive species to occupy environments that are different from those found within native ranges. Here, we assess the potential invadable areas of  the world’s most pervasive invasive amphibians: the cane toad, Rhinella marina?+?R. horribilis, and the North American bullfrog, Lithobates catesbeianus. The uncontrolled spread of such voracious, large-bodied, and disease-tolerant anurans has been documented to impact native faunas worldwide. To disentangle their invasion-related niche dynamics, we compared the predictive ability and distributional forecasts of ecological niche models calibrated with information from native, invaded and pooled (native?+?invaded) ranges. We found that including occurrences from invaded ranges improved model accuracy for both studied species. Non-native occurrences also accounted for 54% and 61% increase in the total area of potential distribution of the cane toad and bullfrog, respectively. Besides, the latter species occupied locations with climatic conditions that are more extreme than those found within its native range. Our results indicate that the occupancy of environments different from those found in native ranges increases the overall potential distribution of the studied invasive anuran species. Therefore, climate information on native ranges alone is insufficient to explain and anticipate the distributional patterns of invasion of cane toads and bullfrogs, underestimating predictions of potential invadable distribution. Moreover, such an observed expansion of realized niches towards occupancy of climates not found within native ranges also has clear implications for invasion risk assessments based on climate modelling worldwide.

     

Comparative mitochondrial genetics of North American and Eurasian mergansers with an emphasis on the endangered scaly-sided merganser (Mergus squamatus)

The scaly-sided merganser, Mergus squamatus, is considered one of the most threatened sea duck species in the Palearctic with limited breeding and wintering distribution in China and Russia. To provide information for future conservation efforts, we sequenced a portion of the mitochondrial (mt) DNA control region in four species of mergansers and three additional sea duck taxa to characterize the evolutionary history of the scaly-sided merganser, infer population trends that may have led to its limited geographic distribution, and to compare indices of genetic diversity among species of mergansers. Scaly-sided mergansers exhibit substantially lower levels of mtDNA genetic diversity (h = 0.292, π = 0.0007) than other closely related sea ducks and many other avian taxa. The four haplotypes observed differed by a single base pair suggesting that the species has not experienced a recent population decline but has instead been at a low population level for some time. A phylogenetic analysis placed the scaly-sided merganser basal to North American and European forms of the common merganser, M. merganser. Our inclusion of a small number of male samples doubled the number of mtDNA haplotypes observed, suggesting that additional genetic variation likely exists within the global population if there is immigration of males from unsampled breeding areas.     

Mining biological networks for unknown pathways

MOTIVATION: Biological pathways provide significant insights on the interaction mechanisms of molecules. Presently, many essential pathways still remain unknown or incomplete for newly sequenced organisms. Moreover, experimental validation of enormous numbers of possible pathway candidates in a wet-lab environment is time- and effort-extensive. Thus, there is a need for comparative genomics tools that help scientists predict pathways in an organism's biological network. RESULTS: In this article, we propose a technique to discover unknown pathways in organisms. Our approach makes in-depth use of Gene Ontology (GO)-based functionalities of enzymes involved in metabolic pathways as follows: i. Model each pathway as a biological functionality graph of enzyme GO functions, which we call pathway functionality template. ii. Locate frequent pathway functionality patterns so as to infer previously unknown pathways through pattern matching in metabolic networks of organisms. We have experimentally evaluated the accuracy of the presented technique for 30 bacterial organisms to predict around 1500 organism-specific versions of 50 reference pathways. Using cross-validation strategy on known pathways, we have been able to infer pathways with 86% precision and 72% recall for enzymes (i.e. nodes). The accuracy of the predicted enzyme relationships has been measured at 85% precision with 64% recall. AVAILABILITY: Code upon request. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Stochastic S-system modeling of gene regulatory network

Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction . Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction . The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomycescerevisiae yeast, and (2) the SOS DNA repair network in Escherichiacoli.     

Inference for nonlinear epidemiological models using genealogies and time series

Phylodynamics - the field aiming to quantitatively integrate the ecological and evolutionary dynamics of rapidly evolving populations like those of RNA viruses - increasingly relies upon coalescent approaches to infer past population dynamics from reconstructed genealogies. As sequence data have become more abundant, these approaches are beginning to be used on populations undergoing rapid and rather complex dynamics. In such cases, the simple demographic models that current phylodynamic methods employ can be limiting. First, these models are not ideal for yielding biological insight into the processes that drive the dynamics of the populations of interest. Second, these models differ in form from mechanistic and often stochastic population dynamic models that are currently widely used when fitting models to time series data. As such, their use does not allow for both genealogical data and time series data to be considered in tandem when conducting inference. Here, we present a flexible statistical framework for phylodynamic inference that goes beyond these current limitations. The framework we present employs a recently developed method known as particle MCMC to fit stochastic, nonlinear mechanistic models for complex population dynamics to gene genealogies and time series data in a Bayesian framework. We demonstrate our approach using a nonlinear Susceptible-Infected-Recovered (SIR) model for the transmission dynamics of an infectious disease and show through simulations that it provides accurate estimates of past disease dynamics and key epidemiological parameters from genealogies with or without accompanying time series data.     

Reconstruction of cell population dynamics using CFSE

Background  

Quantifying cell division and death is central to many studies in the biological sciences. The fluorescent dye CFSE allows the tracking of cell division in vitro and in vivo and provides a rich source of information with which to test models of cell kinetics. Cell division and death have a stochastic component at the single-cell level, and the probabilities of these occurring in any given time interval may also undergo systematic variation at a population level. This gives rise to heterogeneity in proliferating cell populations. Branching processes provide a natural means of describing this behaviour.     

A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks

Background  

The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can simultaneously tackle disparity in time scales and population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo (HyMSMC) method that fills in this void.