4,343 research outputs found
Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes
Multiple biological processes are driven by oscillatory gene expression at
different time scales. Pulsatile dynamics are thought to be widespread, and
single-cell live imaging of gene expression has lead to a surge of dynamic,
possibly oscillatory, data for different gene networks. However, the regulation
of gene expression at the level of an individual cell involves reactions
between finite numbers of molecules, and this can result in inherent randomness
in expression dynamics, which blurs the boundaries between aperiodic
fluctuations and noisy oscillators. Thus, there is an acute need for an
objective statistical method for classifying whether an experimentally derived
noisy time series is periodic. Here we present a new data analysis method that
combines mechanistic stochastic modelling with the powerful methods of
non-parametric regression with Gaussian processes. Our method can distinguish
oscillatory gene expression from random fluctuations of non-oscillatory
expression in single-cell time series, despite peak-to-peak variability in
period and amplitude of single-cell oscillations. We show that our method
outperforms the Lomb-Scargle periodogram in successfully classifying cells as
oscillatory or non-oscillatory in data simulated from a simple genetic
oscillator model and in experimental data. Analysis of bioluminescent live cell
imaging shows a significantly greater number of oscillatory cells when
luciferase is driven by a {\it Hes1} promoter (10/19), which has previously
been reported to oscillate, than the constitutive MoMuLV 5' LTR (MMLV) promoter
(0/25). The method can be applied to data from any gene network to both
quantify the proportion of oscillating cells within a population and to measure
the period and quality of oscillations. It is publicly available as a MATLAB
package.Comment: 36 pages, 17 figure
Phase resetting reveals network dynamics underlying a bacterial cell cycle
Genomic and proteomic methods yield networks of biological regulatory
interactions but do not provide direct insight into how those interactions are
organized into functional modules, or how information flows from one module to
another. In this work we introduce an approach that provides this complementary
information and apply it to the bacterium Caulobacter crescentus, a paradigm
for cell-cycle control. Operationally, we use an inducible promoter to express
the essential transcriptional regulatory gene ctrA in a periodic, pulsed
fashion. This chemical perturbation causes the population of cells to divide
synchronously, and we use the resulting advance or delay of the division times
of single cells to construct a phase resetting curve. We find that delay is
strongly favored over advance. This finding is surprising since it does not
follow from the temporal expression profile of CtrA and, in turn, simulations
of existing network models. We propose a phenomenological model that suggests
that the cell-cycle network comprises two distinct functional modules that
oscillate autonomously and couple in a highly asymmetric fashion. These
features collectively provide a new mechanism for tight temporal control of the
cell cycle in C. crescentus. We discuss how the procedure can serve as the
basis for a general approach for probing network dynamics, which we term
chemical perturbation spectroscopy (CPS)
Synthetic in vitro transcriptional oscillators
The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells
Delays induce novel stochastic effects in negative feedback gene circuits
AbstractStochastic models of reaction networks are widely used to depict gene expression dynamics. However, stochastic does not necessarily imply accurate, as subtle assumptions can yield erroneous results, masking key discrete effects. For instance, transcription and translation are not instantaneous processes—explicit delays separate their initiation from the appearance of their functional products. However, delays are often ignored in stochastic, single-gene expression models. By consequence, effects such as delay-induced stochastic oscillations at the single-cell level have remained relatively unexplored. Here, we present a systematic study of periodicity and multimodality in a simple gene circuit with negative feedback, analyzing the influence of negative feedback strength and transcriptional/translational delays on expression dynamics. We demonstrate that an oscillatory regime emerges through a Hopf bifurcation in both deterministic and stochastic frameworks. Of importance, a shift in the stochastic Hopf bifurcation evidences inaccuracies of the deterministic bifurcation analysis. Furthermore, noise fluctuations within stochastic oscillations decrease alongside increasing values of transcriptional delays and within a specific range of negative feedback strengths, whereas a strong feedback is associated with oscillations triggered by bursts. Finally, we demonstrate that explicitly accounting for delays increases the number of accessible states in the multimodal regime, and also introduces features typical of excitable systems
Delay-dependent Stability of Genetic Regulatory Networks
Genetic regulatory networks are biochemical reaction systems, consisting of a network of interacting genes and associated proteins. The dynamics of genetic regulatory networks contain many complex facets that require careful consideration during the modeling process. The classical modeling approach involves studying systems of ordinary differential equations (ODEs) that model biochemical reactions in a deterministic, continuous, and instantaneous fashion. In reality, the dynamics of these systems are stochastic, discrete, and widely delayed. The first two complications are often successfully addressed by modeling regulatory networks using the Gillespie stochastic simulation algorithm (SSA), while the delayed behavior of biochemical events such as transcription and translation are often ignored due to their mathematically difficult nature. We develop techniques based on delay-differential equations (DDEs) and the delayed Gillespie SSA to study the effects of delays, in both continuous deterministic and discrete stochastic settings. Our analysis applies techniques from Floquet theory and advanced numerical analysis within the context of delay-differential equations, and we are able to derive stability sensitivities for biochemical switches and oscillators across the constituent pathways, showing which pathways in the regulatory networks improve or worsen the stability of the system attractors. These delay sensitivities can be far from trivial, and we offer a computational framework validated across multiple levels of modeling fidelity. This work suggests that delays may play an important and previously overlooked role in providing robust dynamical behavior for certain genetic regulatory networks, and perhaps more importantly, may offer an accessible tuning parameter for robust bioengineering
Oscillations and temporal signalling in cells
The development of new techniques to quantitatively measure gene expression
in cells has shed light on a number of systems that display oscillations in
protein concentration. Here we review the different mechanisms which can
produce oscillations in gene expression or protein concentration, using a
framework of simple mathematical models. We focus on three eukaryotic genetic
regulatory networks which show "ultradian" oscillations, with time period of
the order of hours, and involve, respectively, proteins important for
development (Hes1), apoptosis (p53) and immune response (NFkB). We argue that
underlying all three is a common design consisting of a negative feedback loop
with time delay which is responsible for the oscillatory behaviour
Symmetries, Stability, and Control in Nonlinear Systems and Networks
This paper discusses the interplay of symmetries and stability in the
analysis and control of nonlinear dynamical systems and networks. Specifically,
it combines standard results on symmetries and equivariance with recent
convergence analysis tools based on nonlinear contraction theory and virtual
dynamical systems. This synergy between structural properties (symmetries) and
convergence properties (contraction) is illustrated in the contexts of network
motifs arising e.g. in genetic networks, of invariance to environmental
symmetries, and of imposing different patterns of synchrony in a network.Comment: 16 pages, second versio
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