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)

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field

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

Oscillations and temporal signalling in cells

ArXiv pre-print: http://arxiv.org/abs/q-bio/0703047.-- Final full-text version of the paper available at: http://dx.doi.org/10.1088/1478-3975/4/2/R01.PMID: 17664651The 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 a time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NF-κB). 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.SK, MHJ and KS acknowledge support from the Danish National Research Foundation and Villum Kann Rasmussen Foundation. GT acknowledges support from the FIRB 2003 program of the Italian Ministry for University and Scientific Research

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

Doctor of Philosophy

dissertationWe formulate and analyze three spatio-temporal models for cell polarization in budding yeast, fission yeast, and the neuronal growth cone, respectively. We focus on the roles of diffusion and active transport of cytosolic molecules along cytoskeletal filaments on the establishment of a polarized distribution of membrane-bound molecules. Our first model couples the diffusion equation on a finite interval to a pair of delay differential equations at the boundaries. The model is used to study the oscillatory dynamics of the signaling molecule Cdc42 in fission yeast. We explore the effect of diffusion by performing a bifurcation analysis and find that the critical time delay for the onset of oscillations increases as the diffusion coefficient decreases. We then extend the model to a growing domain and show that there is a transition from asymmetric to symmetric oscillations as the cell grows. This is consistent with the experimental findings of “new-end-takeoff†in fission yeast. In our second model, we study the active transport of signaling molecules along a two-dimensional microtubule (MT) network in the neuronal growth cone. We consider a Rac1-stathmin-MT pathway and use a modified Dogteromâ€"Leibler model for the microtubule growth. In the presence of a nonuniform Rac1 concentration, we derive the resulting nonuniform length distribution of MTs and couple it to the active transport model. We calculate the polarized distribution of signaling molecules at the membrane using perturbation analysis and numerical simulation. We find the distribution is sensitive to the explicit Rac1 distribution and the stahmin-MT pathway. Our third model is a stochastic active transport model for vesicles containing signaling molecules in a filament network. We first derive the corresponding advection-diffusion model by a quasi-steady-state analysis. We find the diffusion is anisotropic and depends on the local density of filaments. The stability of the homogeneous steady state is sensitive to the geometry of filaments. For a parallelMTnetwork, the homogeneous steady state is linearly stable. For a network with filaments nucleated from the membrane (actin cytoskeleton), the homogeneous steady state is linearly unstable and a polarized distribution can occur

Reliability of Transcriptional Cycles and the Yeast Cell-Cycle Oscillator

A recently published transcriptional oscillator associated with the yeast cell cycle provides clues and raises questions about the mechanisms underlying autonomous cyclic processes in cells. Unlike other biological and synthetic oscillatory networks in the literature, this one does not seem to rely on a constitutive signal or positive auto-regulation, but rather to operate through stable transmission of a pulse on a slow positive feedback loop that determines its period. We construct a continuous-time Boolean model of this network, which permits the modeling of noise through small fluctuations in the timing of events, and show that it can sustain stable oscillations. Analysis of simpler network models shows how a few building blocks can be arranged to provide stability against fluctuations. Our findings suggest that the transcriptional oscillator in yeast belongs to a new class of biological oscillators