David Adalsteinsson

A bottom-up approach to gene regulation.

The ability to construct synthetic gene networks enables experimental investigations of deliberately simplified systems that can be compared to qualitative and quantitative models. If simple, well-characterized modules can be coupled together into more complex networks with behaviour that can be predicted from that of the individual components, we may begin to build an understanding of cellular regulatory processes from the ‘bottom up’. Here we have engineered a promoter to allow simultaneous repression and activation of gene expression in Escherichia coli. We studied its behaviour in synthetic gene networks under increasingly complex conditions: unregulated, repressed, activated, and simultaneously repressed and activated. We develop a stochastic model that quantitatively captures the means and distributions of the expression from the engineered promoter of this modular system, and show that the model can be extended and used to accurately predict the in vivo behaviour of the network when it is expanded to include positive feedback. The model also reveals the counterintuitive prediction that noise in protein expression levels can increase upon arrest of cell growth and division, which we confirm experimentally. This work shows that the properties of regulatory subsystems can be used to predict the behaviour of larger, more complex regulatory networks, and that this bottom-up approach can provide insights into gene regulation.

An overview of level set methods for etching, deposition, and lithography development

The range of surface evolution problems in etching, deposition, and lithography development offers significant challenge for numerical methods in front tracking. Level set methods for evolving interfaces are specifically designed for profiles which can develop sharp corners, change topology, and undergo orders of magnitude changes in speed. They are based on solving a Hamilton-Jacobi type equation for a level set function, using techniques borrowed from hyperbolic conservation laws. Over the past few years, a body of level set methods have been developed with application to microfabrication problems. In this paper, we give an overview of these techniques, describe the implementation in etching, deposition, and lithography simulations, and present a collection of fast level set methods, each aimed at a particular application. In the case of photoresist development and isotropic etching/deposition, the fast marching level set method, introduced by Sethian (1996), can track the three-dimensional photoresist process through a 200/spl times/200/spl times/200 rate function grid in under 55 s on a Sparc10. In the case of more complex etching and deposition, the narrow band level set method, introduced in Adalsteinsson and Sethian (1995), can be used to handle problems in which the speed of the interface delicately depends on the orientation of the interface versus an incoming beam, the effects of visibility, surface tension, reflection and re-emission, and complex three-dimensional effects. Our applications include photoresist development, etching/deposition problems under the effects of masking, visibility, complex flux integrations over sources, nonconvex sputter deposition problems, and simultaneous deposition and etch phenomena.

Biochemical Network Stochastic Simulator (BioNetS): software for stochastic modeling of biochemical networks

BackgroundIntrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA) molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks.ResultsWe have developed the software package Biochemical Network Stochastic Simulator (BioNetS) for efficientlyand accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous) for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solvesthe appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS.ConclusionsWe have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.

Transport and diffusion of material quantities on propagating interfaces via level set methods

We develop theory and numerical algorithms to apply level set methods to problems involving the transport and diffusion of material quantities in a level set framework. Level set methods are computational techniques for tracking moving interfaces; they work by embedding the propagating interface as the zero level set of a higher dimensional function, and then approximate the solution of the resulting initial value partial differential equation using upwind finite difference schemes. The traditional level set method works in the trace space of the evolving interface, and hence disregards any parameterization in the interface description. Consequently, material quantities on the interface which themselves are transported under the interface motion are not easily handled in this framework. We develop model equations and algorithmic techniques to extend the level set method to include these problems. We demonstrate the accuracy of our approach through a series of test examples and convergence studies.

An internal splash: Levitation of falling spheres in stratified fluids

We experimentally explore the motion of falling spheres in strongly stratified fluids in which the fluid transitions from low density at the top to high density at the bottom and document an internal splash in which the falling sphere may reverse its direction of motion (from falling, to rising, to falling again) as it penetrates a region of strong density transition. We present measurements of the sphere’s velocity and exhibit nonmonotonic sphere velocity profiles connecting the maximum and minimum terminal velocities, matching earlier measurements [J. Fluid Mech. 381, 175 (1999)], but further exhibit the new levitation phenomenon. We give a physical explanation of this motion which necessarily couples the sphere motion with the stratified fluid, and vice versa, and supplement this with a simplified, reduced mathematical model involving a nonlinear system of ordinary differential equations which captures the nonmonotonic transition and agrees with the measured velocity profiles at all depths except those...

A coupled level set-boundary integral method for moving boundary simulations

A numerical method for moving boundary problems based upon level set and boundary integral formulations is presented. The interface velocity is obtained from the boundary integral solution using a Galerkin technique for post-processing function gradients on the interface. We introduce a new level set technique for propagating free boundary values in time, and couple this to a narrow band level set method. Together, they allow us to both update the function values and the location of the interface. The methods are discussed in the context of the well-studied two-dimensional nonlinear potential flow model of breaking waves over a sloping beach. The numerical results show wave breaking and rollup, and the algorithm is verified by means of convergence studies and comparisons with previous techniques. 1. Introduction and overview

Subsurface Trapping of Oil Plumes in Stratification: Laboratory Investigations

Laboratory experiments demonstrating how the addition of surfactants creates the possibility of trapping buoyant immiscible fluids are presented. In particular, these experiments demonstrate that buoyant immiscible plumes like those which occurred during the Deepwater Horizon Gulf oil spill can be trapped as they rise through an ambient, stratified fluid. The addition of surfactants is an important mechanism by which trapping can occur. In this paper, we describe experiments and theory on trapping/escape of plumes containing an oil/water/surfactant mixture released into nonlinear stratification. We also present results on the timescale for trapping and for destabilization and release of trapped subsurface plumes. This timescale is shown to be a function of the oil to surfactant ratio.

Modelling a growth instability in a stressed solid

The growth of crystalline silicon from the amorphous phase in the presence of an applied stress is modelled using advanced numerical methods. The crystal region is modelled as a linear elastic solid and the amorphous as a viscous fluid with a time-dependent viscosity to reflect structural relaxation. Appropriate coupling conditions across the boundary are defined, and both problems are solved using a symmetric-Galerkin boundary integral method. The interface is advanced in time using the level set technique. The results match well with experiments and support the proposed kinetic mechanism for the observed interface growth instability.

Entropy gives rise to topologically associating domains

We investigate chromosome organization within the nucleus using polymer models whose formulation is closely guided by experiments in live yeast cells. We employ bead-spring chromosome models together with loop formation within the chains and the presence of nuclear bodies to quantify the extent to which these mechanisms shape the topological landscape in the interphase nucleus. By investigating the genome as a dynamical system, we show that domains of high chromosomal interactions can arise solely from the polymeric nature of the chromosome arms due to entropic interactions and nuclear confinement. In this view, the role of bio-chemical related processes is to modulate and extend the duration of the interacting domains.

Enrichment of dynamic chromosomal crosslinks drive phase separation of the nucleolus

Abstract Regions of highly repetitive DNA, such as those found in the nucleolus, show a self-organization that is marked by spatial segregation and frequent self-interaction. The mechanisms that underlie the sequestration of these sub-domains are largely unknown. Using a stochastic, bead-spring representation of chromatin in budding yeast, we find enrichment of protein-mediated, dynamic chromosomal cross-links recapitulates the segregation, morphology and self-interaction of the nucleolus. Rates and enrichment of dynamic crosslinking have profound consequences on domain morphology. Our model demonstrates the nucleolus is phase separated from other chromatin in the nucleus and predicts that multiple rDNA loci will form a single nucleolus independent of their location within the genome. Fluorescent labeling of budding yeast nucleoli with CDC14-GFP revealed that a split rDNA locus indeed forms a single nucleolus. We propose that nuclear sub-domains, such as the nucleolus, result from phase separations within the nucleus, which are driven by the enrichment of protein-mediated, dynamic chromosomal crosslinks.