In Silico Synchronization of Cellular Populations Through Expression Data Deconvolution

Cellular populations are typically heterogenous collections of cells at different points in their respective cell cycles, each with a cell cycle time that varies from individual to individual. As a result, true single-cell behavior, particularly that which is cell-cycle--dependent, is often obscured in population-level (averaged) measurements. We have developed a simple deconvolution method that can be used to remove the effects of asynchronous variability from population-level time-series data. In this paper, we summarize some recent progress in the development and application of our approach, and provide technical updates that result in increased biological fidelity. We also explore several preliminary validation results and discuss several ongoing applications that highlight the method's usefulness for estimating parameters in differential equation models of single-cell gene regulation.Comment: accepted for the 48th ACM/IEEE Design Automation Conferenc

Pulsars Cannot Account for the Inner Galaxy's GeV Excess

Using data from the Fermi Gamma-Ray Space Telescope, a spatially extended component of gamma rays has been identified from the direction of the Galactic Center, peaking at energies of ~2-3 GeV. More recently, it has been shown that this signal is not confined to the innermost hundreds of parsecs of the Galaxy, but instead extends to at least ~3 kpc from the Galactic Center. While the spectrum, intensity, and angular distribution of this signal is in good agreement with predictions from annihilating dark matter, it has also been suggested that a population of unresolved millisecond pulsars could be responsible for this excess GeV emission from the Inner Galaxy. In this paper, we consider this later possibility in detail. Comparing the observed spectral shape of the Inner Galaxy's GeV excess to the spectrum measured from 37 millisecond pulsars by Fermi, we find that these sources exhibit a spectral shape that is much too soft at sub-GeV energies to accommodate this signal. We also construct population models to describe the spatial distribution and luminosity function of the Milky Way's millisecond pulsars. After taking into account constraints from the observed distribution of Fermi sources (including both sources known to be millisecond pulsars, and unidentified sources which could be pulsars), we find that millisecond pulsars can account for no more than ~10% of the Inner Galaxy's GeV excess. Each of these arguments strongly disfavor millisecond pulsars as the source of this signal.Comment: 13 pages, 11 figure

Biomolecular resource utilization in elementary cell-free gene circuits

We present a detailed dynamical model of the behavior of transcription-translation circuits in vitro that makes explicit the roles played by essential molecular resources. A set of simple two-gene test circuits operating in a cell-free biochemical 'breadboard' validate this model and highlight the consequences of limited resource availability. In particular, we are able to confirm the existence of biomolecular 'crosstalk' and isolate its individual sources. The implications of crosstalk for biomolecular circuit design and function are discussed

Emergence of switch-like behavior in a large family of simple biochemical networks

Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can exhibit bistability remains a challenge, in part due to the exceedingly large variety of GRNs that exist for even a small number of components. We begin to address this problem by employing chemical reaction network theory in a comprehensive in silico survey to determine the capacity for bistability of more than 40,000 simple networks that can be formed by two transcription factor-coding genes and their associated proteins (assuming only the most elementary biochemical processes). We find that there exist reaction rate constants leading to bistability in ~90% of these GRN models, including several circuits that do not contain any of the TF cooperativity commonly associated with bistable systems, and the majority of which could only be identified as bistable through an original subnetwork-based analysis. A topological sorting of the two-gene family of networks based on the presence or absence of biochemical reactions reveals eleven minimal bistable networks (i.e., bistable networks that do not contain within them a smaller bistable subnetwork). The large number of previously unknown bistable network topologies suggests that the capacity for switch-like behavior in GRNs arises with relative ease and is not easily lost through network evolution. To highlight the relevance of the systematic application of CRNT to bistable network identification in real biological systems, we integrated publicly available protein-protein interaction, protein-DNA interaction, and gene expression data from Saccharomyces cerevisiae, and identified several GRNs predicted to behave in a bistable fashion.Comment: accepted to PLoS Computational Biolog

The capacity for multistability in small gene regulatory networks

<p>Abstract</p> <p>Background</p> <p>Recent years have seen a dramatic increase in the use of mathematical modeling to gain insight into gene regulatory network behavior across many different organisms. In particular, there has been considerable interest in using mathematical tools to understand how multistable regulatory networks may contribute to developmental processes such as cell fate determination. Indeed, such a network may subserve the formation of unicellular leaf hairs (trichomes) in the model plant <it>Arabidopsis thaliana</it>.</p> <p>Results</p> <p>In order to investigate the capacity of small gene regulatory networks to generate multiple equilibria, we present a chemical reaction network (CRN)-based modeling formalism and describe a number of methods for CRN analysis in a parameter-free context. These methods are compared and applied to a full set of one-component subnetworks, as well as a large random sample from 40,680 similarly constructed two-component subnetworks. We find that positive feedback and cooperativity mediated by transcription factor (TF) dimerization is a requirement for one-component subnetwork bistability. For subnetworks with two components, the presence of these processes increases the probability that a randomly sampled subnetwork will exhibit multiple equilibria, although we find several examples of bistable two-component subnetworks that do not involve cooperative TF-promoter binding. In the specific case of epidermal differentiation in <it>Arabidopsis</it>, dimerization of the GL3-GL1 complex and cooperative sequential binding of GL3-GL1 to the CPC promoter are each independently sufficient for bistability.</p> <p>Conclusion</p> <p>Computational methods utilizing CRN-specific theorems to rule out bistability in small gene regulatory networks are far superior to techniques generally applicable to deterministic ODE systems. Using these methods to conduct an unbiased survey of parameter-free deterministic models of small networks, and the <it>Arabidopsis </it>epidermal cell differentiation subnetwork in particular, we illustrate how future experimental research may be guided by network structure analysis.</p

Model-Based Deconvolution of Cell Cycle Time-Series Data Reveals Gene Expression Details at High Resolution

In both prokaryotic and eukaryotic cells, gene expression is regulated across the cell cycle to ensure “just-in-time” assembly of select cellular structures and molecular machines. However, present in all time-series gene expression measurements is variability that arises from both systematic error in the cell synchrony process and variance in the timing of cell division at the level of the single cell. Thus, gene or protein expression data collected from a population of synchronized cells is an inaccurate measure of what occurs in the average single-cell across a cell cycle. Here, we present a general computational method to extract “single-cell”-like information from population-level time-series expression data. This method removes the effects of 1) variance in growth rate and 2) variance in the physiological and developmental state of the cell. Moreover, this method represents an advance in the deconvolution of molecular expression data in its flexibility, minimal assumptions, and the use of a cross-validation analysis to determine the appropriate level of regularization. Applying our deconvolution algorithm to cell cycle gene expression data from the dimorphic bacterium Caulobacter crescentus, we recovered critical features of cell cycle regulation in essential genes, including ctrA and ftsZ, that were obscured in population-based measurements. In doing so, we highlight the problem with using population data alone to decipher cellular regulatory mechanisms and demonstrate how our deconvolution algorithm can be applied to produce a more realistic picture of temporal regulation in a cell.</p

An analytical approach to bistable biological circuit discrimination using real algebraic geometry

Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining which bistable circuit design out of many is best for their specific application. In this work we explore the applicability of Sturm's theorem—a tool from nineteenth-century real algebraic geometry—to comparing ‘functionally equivalent’ bistable circuits without the need for numerical simulation. We first consider two genetic toggle variants and two different positive feedback circuits, and show how specific topological properties present in each type of circuit can serve to increase the size of the regions of parameter space in which they function as switches. We then demonstrate that a single competitive monomeric activator added to a purely monomeric (and otherwise monostable) mutual repressor circuit is sufficient for bistability. Finally, we compare our approach with the Routh–Hurwitz method and derive consistent, yet more powerful, parametric conditions. The predictive power and ease of use of Sturm's theorem demonstrated in this work suggest that algebraic geometric techniques may be underused in biomolecular circuit analysis

Gene Circuit Performance Characterization and Resource Usage in a Cell-Free “Breadboard”

The many successes of synthetic biology have come in a manner largely different from those in other engineering disciplines; in particular, without well-characterized and simplified prototyping environments to play a role analogous to wind-tunnels in aerodynamics and breadboards in electrical engineering. However, as the complexity of synthetic circuits increases, the benefits—in cost savings and design cycle time—of a more traditional engineering approach can be significant. We have recently developed an in vitro “breadboard” prototyping platform based on E. coli cell extract that allows biocircuits to operate in an environment considerably simpler than, but functionally similar to, in vivo. The simplicity of this system makes it a promising tool for rapid biocircuit design and testing, as well as for probing fundamental aspects of gene circuit operation normally masked by cellular complexity. In this work, we characterize the cell-free breadboard using real-time and simultaneous measurements of transcriptional and translational activities of a small set of reporter genes and a transcriptional activation cascade. We determine the effects of promoter strength, gene concentration, and nucleoside triphosphate concentration on biocircuit properties, and we isolate the specific contributions of essential biomolecular resources—core RNA polymerase and ribosomes—to overall performance. Importantly, we show how limits on resources, particularly those involved in translation, are manifested as reduced expression in the presence of orthogonal genes that serve as additional loads on the system

Minimally invasive determination of mRNA concentration in single living bacteria

Fluorescence correlation spectroscopy (FCS) has permitted the characterization of high concentrations of noncoding RNAs in a single living bacterium. Here, we extend the use of FCS to low concentrations of coding RNAs in single living cells. We genetically fuse a red fluorescent protein (RFP) gene and two binding sites for an RNA-binding protein, whose translated product is the RFP protein alone. Using this construct, we determine in single cells both the absolute [mRNA] concentration and the associated [RFP] expressed from an inducible plasmid. We find that the FCS method allows us to reliably monitor in real-time [mRNA] down to ∼40 nM (i.e. approximately two transcripts per volume of detection). To validate these measurements, we show that [mRNA] is proportional to the associated expression of the RFP protein. This FCS-based technique establishes a framework for minimally invasive measurements of mRNA concentration in individual living bacteria

Model-Based Deconvolution of Cell Cycle Time-Series Data Reveals Gene Expression Details at High Resolution

In both prokaryotic and eukaryotic cells, gene expression is regulated across the cell cycle to ensure “just-in-time” assembly of select cellular structures and molecular machines. However, present in all time-series gene expression measurements is variability that arises from both systematic error in the cell synchrony process and variance in the timing of cell division at the level of the single cell. Thus, gene or protein expression data collected from a population of synchronized cells is an inaccurate measure of what occurs in the average single-cell across a cell cycle. Here, we present a general computational method to extract “single-cell”-like information from population-level time-series expression data. This method removes the effects of 1) variance in growth rate and 2) variance in the physiological and developmental state of the cell. Moreover, this method represents an advance in the deconvolution of molecular expression data in its flexibility, minimal assumptions, and the use of a cross-validation analysis to determine the appropriate level of regularization. Applying our deconvolution algorithm to cell cycle gene expression data from the dimorphic bacterium Caulobacter crescentus, we recovered critical features of cell cycle regulation in essential genes, including ctrA and ftsZ, that were obscured in population-based measurements. In doing so, we highlight the problem with using population data alone to decipher cellular regulatory mechanisms and demonstrate how our deconvolution algorithm can be applied to produce a more realistic picture of temporal regulation in a cell