23,660 research outputs found
Bistability of an In Vitro Synthetic Autoregulatory Switch
The construction of synthetic biochemical circuits is an essential step for developing quantitative understanding
of information processing in natural organisms. Here, we report construction and analysis of an in vitro circuit with
positive autoregulation that consists of just four synthetic DNA strands and three enzymes, bacteriophage T7 RNA
polymerase, Escherichia coli ribonuclease (RNase) H, and RNase R. The modularity of the DNA switch template allowed
a rational design of a synthetic DNA switch regulated by its RNA output acting as a transcription activator. We verified
that the thermodynamic and kinetic constraints dictated by the sequence design criteria were enough to experimentally
achieve the intended dynamics: a transcription activator configured to regulate its own production. Although only
RNase H is necessary to achieve bistability of switch states, RNase R is necessary to maintain stable RNA signal levels and
to control incomplete degradation products. A simple mathematical model was used to fit ensemble parameters for the
training set of experimental results and was then directly applied to predict time-courses of switch dynamics and sensitivity
to parameter variations with reasonable agreement. The positive autoregulation switches can be used to provide constant
input signals and store outputs of biochemical networks and are potentially useful for chemical control applications
Stochastic Gene Expression in a Lentiviral Positive Feedback Loop: HIV-1 Tat Fluctuations Drive Phenotypic Diversity
Stochastic gene expression has been implicated in a variety of cellular
processes, including cell differentiation and disease. In this issue of Cell,
Weinberger et al. (2005) take an integrated computational-experimental approach
to study the Tat transactivation feedback loop in HIV-1 and show that
fluctuations in a key regulator, Tat, can result in a phenotypic bifurcation.
This phenomenon is observed in an isogenic population where individual cells
display two distinct expression states corresponding to latent and productive
infection by HIV-1. These findings demonstrate the importance of stochastic
gene expression in molecular "decision-making."Comment: Supplemental data available as q-bio.MN/060800
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
Isolating intrinsic noise sources in a stochastic genetic switch
The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule that binds to the promotor of the other gene. When the repressor is bound to a promotor, the corresponding gene is not transcribed and no protein is produced. Either one of the promotors can be repressed at any given time or both can be unrepressed, leaving three possible promotor states. This model is analysed in its bistable regime in which the deterministic limit exhibits two stable fixed points and an unstable saddle, and the case of small noise is considered. On small time scales, the stochastic process fluctuates near one of the stable fixed points, and on large time scales, a metastable transition can occur, where fluctuations drive the system past the unstable saddle to the other stable fixed point. To explore how different intrinsic noise sources affect these transitions, fluctuations in protein production and degradation are eliminated, leaving fluctuations in the promotor state as the only source of noise in the system. Perturbation methods are then used to compute the stability landscape and the distribution of transition times, or first exit time density. To understand how protein noise affects the system, small magnitude fluctuations are added back into the process, and the stability landscape is compared to that of the process without protein noise. It is found that significant differences in the random process emerge in the presence of protein noise
Strongly nonlinear dynamics of electrolytes in large ac voltages
We study the response of a model micro-electrochemical cell to a large ac
voltage of frequency comparable to the inverse cell relaxation time. To bring
out the basic physics, we consider the simplest possible model of a symmetric
binary electrolyte confined between parallel-plate blocking electrodes,
ignoring any transverse instability or fluid flow. We analyze the resulting
one-dimensional problem by matched asymptotic expansions in the limit of thin
double layers and extend previous work into the strongly nonlinear regime,
which is characterized by two novel features - significant salt depletion in
the electrolyte near the electrodes and, at very large voltage, the breakdown
of the quasi-equilibrium structure of the double layers. The former leads to
the prediction of "ac capacitive desalination", since there is a time-averaged
transfer of salt from the bulk to the double layers, via oscillating diffusion
layers. The latter is associated with transient diffusion limitation, which
drives the formation and collapse of space-charge layers, even in the absence
of any net Faradaic current through the cell. We also predict that steric
effects of finite ion sizes (going beyond dilute solution theory) act to
suppress the strongly nonlinear regime in the limit of concentrated
electrolytes, ionic liquids and molten salts. Beyond the model problem, our
reduced equations for thin double layers, based on uniformly valid matched
asymptotic expansions, provide a useful mathematical framework to describe
additional nonlinear responses to large ac voltages, such as Faradaic
reactions, electro-osmotic instabilities, and induced-charge electrokinetic
phenomena.Comment: 30 pages, 17 eps-figures, RevTe
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
Numerical algebraic geometry for model selection and its application to the life sciences
Researchers working with mathematical models are often confronted by the
related problems of parameter estimation, model validation, and model
selection. These are all optimization problems, well-known to be challenging
due to non-linearity, non-convexity and multiple local optima. Furthermore, the
challenges are compounded when only partial data is available. Here, we
consider polynomial models (e.g., mass-action chemical reaction networks at
steady state) and describe a framework for their analysis based on optimization
using numerical algebraic geometry. Specifically, we use probability-one
polynomial homotopy continuation methods to compute all critical points of the
objective function, then filter to recover the global optima. Our approach
exploits the geometric structures relating models and data, and we demonstrate
its utility on examples from cell signaling, synthetic biology, and
epidemiology.Comment: References added, additional clarification
- …